80:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000 Sistemas de ecuaciones:@0.073089:0.043661:0.282490:0.043661:0.282490:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En el método sustitutivo de la primera ecuación obtenemos::@0.293660:0.136836:0.731871:0.136836:0.731871:0.120402:0.293660:0.120402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.552098:0.160163:0.559553:0.160163:0.559553:0.143756:0.552098:0.143756:0.000000 = (5 – + ).:@0.559479:0.160163:0.668470:0.160161:0.668470:0.143727:0.559479:0.143729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.581314:0.152324:0.589480:0.152324:0.589480:0.137385:0.581314:0.137385:0.000000 2:@0.581314:0.168714:0.589480:0.168714:0.589480:0.153774:0.581314:0.153774:0.000000 y:@0.627109:0.160161:0.634583:0.160161:0.634583:0.143755:0.627109:0.143755:0.000000 z:@0.653303:0.160161:0.660537:0.160161:0.660537:0.143755:0.653303:0.143755:0.000000 Reemplazamos en la segunda y tercera ecuaciones del último sistema, lo que da lugar :@0.293662:0.187523:0.931276:0.187523:0.931276:0.171089:0.293662:0.171089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.408854:0.187523:0.416309:0.187523:0.416309:0.171117:0.408854:0.171117:0.000000 al siguiente par de ecuaciones::@0.293643:0.204165:0.516327:0.204165:0.516327:0.187731:0.293643:0.187731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (5 – + ) + 2 + 2 = 3,:@0.364787:0.226590:0.564503:0.226597:0.564503:0.210164:0.364787:0.210156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.379696:0.219653:0.387862:0.219653:0.387862:0.204713:0.379696:0.204713:0.000000 2:@0.379696:0.236043:0.387862:0.236043:0.387862:0.221103:0.379696:0.221103:0.000000 y:@0.425491:0.226597:0.432965:0.226597:0.432965:0.210191:0.425491:0.210191:0.000000 z:@0.451685:0.226597:0.458919:0.226597:0.458919:0.210191:0.451685:0.210191:0.000000 y:@0.491334:0.226597:0.498807:0.226597:0.498807:0.210191:0.491334:0.210191:0.000000 z:@0.526418:0.226597:0.533652:0.226597:0.533652:0.210191:0.526418:0.210191:0.000000 – (5 – + ) + + = 0,:@0.364784:0.252600:0.559777:0.252602:0.559777:0.236168:0.364784:0.236167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.392768:0.245659:0.400934:0.245659:0.400934:0.230719:0.392768:0.230719:0.000000 2:@0.392768:0.262048:0.400934:0.262048:0.400934:0.247109:0.392768:0.247109:0.000000 y:@0.438565:0.252602:0.446039:0.252602:0.446039:0.236196:0.438565:0.236196:0.000000 z:@0.464759:0.252602:0.471993:0.252602:0.471993:0.236196:0.464759:0.236196:0.000000 y:@0.495499:0.252602:0.502972:0.252602:0.502972:0.236196:0.495499:0.236196:0.000000 z:@0.521693:0.252602:0.528927:0.252602:0.528927:0.236196:0.521693:0.236196:0.000000 de las que, luego de realizar algunas simplificaciones, se obtiene: :@0.293627:0.288104:0.764352:0.288104:0.764352:0.271670:0.293627:0.271670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.781519:0.264516:0.789685:0.264516:0.789685:0.249576:0.781519:0.249576:0.000000 2:@0.781519:0.280905:0.789685:0.280905:0.789685:0.265966:0.781519:0.265966:0.000000 3:@0.781519:0.296183:0.789685:0.296183:0.789685:0.281243:0.781519:0.281243:0.000000 2:@0.781519:0.312573:0.789685:0.312573:0.789685:0.297633:0.781519:0.297633:0.000000 5:@0.831932:0.264516:0.840098:0.264516:0.840098:0.249576:0.831932:0.249576:0.000000 2:@0.831932:0.280905:0.840098:0.280905:0.840098:0.265966:0.831932:0.265966:0.000000 1:@0.831932:0.296183:0.840098:0.296183:0.840098:0.281243:0.831932:0.281243:0.000000 2:@0.831932:0.312573:0.840098:0.312573:0.840098:0.297633:0.831932:0.297633:0.000000 1:@0.877324:0.264516:0.885490:0.264516:0.885490:0.249576:0.877324:0.249576:0.000000 2:@0.877324:0.280905:0.885490:0.280905:0.885490:0.265966:0.877324:0.265966:0.000000 5:@0.877324:0.296183:0.885490:0.296183:0.885490:0.281243:0.877324:0.281243:0.000000 2:@0.877324:0.312573:0.885490:0.312573:0.885490:0.297633:0.877324:0.297633:0.000000 y:@0.802982:0.276498:0.810455:0.276498:0.810455:0.260092:0.802982:0.260092:0.000000 + = :@0.810382:0.276498:0.875047:0.276498:0.875047:0.260064:0.810382:0.260064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.848927:0.276498:0.856161:0.276498:0.856161:0.260092:0.848927:0.260092:0.000000 y:@0.802964:0.303860:0.810437:0.303860:0.810437:0.287454:0.802964:0.287454:0.000000 + = .:@0.810363:0.303860:0.893914:0.303860:0.893914:0.287426:0.810363:0.287426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.848908:0.303860:0.856142:0.303860:0.856142:0.287454:0.848908:0.287454:0.000000 De la primera ecuación del sistema precedente obtenemos : = – = – :@0.293635:0.339265:0.916923:0.339265:0.916923:0.322831:0.293635:0.322831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y y:@0.724880:0.339265:0.746564:0.339265:0.746564:0.322859:0.724880:0.322859:0.000000:0.000000:0.000000 z :@0.816493:0.339265:0.848706:0.339265:0.848706:0.322859:0.816493:0.322859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z.:@0.904093:0.339265:0.926881:0.339265:0.926881:0.322859:0.904093:0.322859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Reemplazamos en la segunda ecuación: – + = :@0.293635:0.373769:0.776611:0.373771:0.776611:0.357337:0.293635:0.357335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.408864:0.373769:0.416338:0.373769:0.416338:0.357363:0.408864:0.357363:0.000000 z :@0.663112:0.373771:0.698417:0.373771:0.698417:0.357364:0.663112:0.357364:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.732949:0.373771:0.740183:0.373771:0.740183:0.357364:0.732949:0.357364:0.000000 ,:@0.762843:0.373771:0.779869:0.373771:0.779869:0.357364:0.762843:0.357364:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.293660:0.404707:0.297691:0.404707:0.297691:0.388273:0.293660:0.388273:0.000000 – + = :@0.606583:0.404707:0.769421:0.404707:0.769421:0.388273:0.606583:0.388273:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z :@0.659161:0.404707:0.691227:0.404707:0.691227:0.388301:0.659161:0.388301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.725759:0.404707:0.732993:0.404707:0.732993:0.388301:0.725759:0.388301:0.000000 ,:@0.755652:0.404707:0.772679:0.404707:0.772679:0.388301:0.755652:0.388301:0.000000:0.000000:0.000000:0.000000:0.000000 donde = –1.:@0.293648:0.424927:0.393029:0.424927:0.393029:0.408493:0.293648:0.408493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.345815:0.424927:0.353049:0.424927:0.353049:0.408520:0.345815:0.408520:0.000000 Calculamos e . Como = – , y, = –1, se sigue que: = – (–1) = 2.:@0.293648:0.452288:0.862745:0.452288:0.862745:0.435855:0.293648:0.435855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.381451:0.452288:0.413056:0.452288:0.413056:0.435882:0.381451:0.435882:0.000000:0.000000:0.000000 y:@0.468720:0.452288:0.476193:0.452288:0.476193:0.435882:0.468720:0.435882:0.000000 z:@0.543545:0.452288:0.550779:0.452288:0.550779:0.435882:0.543545:0.435882:0.000000 z:@0.580139:0.452288:0.587373:0.452288:0.587373:0.435882:0.580139:0.435882:0.000000 y:@0.729256:0.452288:0.736729:0.452288:0.736729:0.435882:0.729256:0.435882:0.000000 Como = (5 – + ) con = 2, = –1, se obtiene: = (5 – 2 – 1) = 1.:@0.293612:0.479650:0.816470:0.479650:0.816470:0.463217:0.293612:0.463217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.342280:0.479650:0.349735:0.479650:0.349735:0.463244:0.342280:0.463244:0.000000 y:@0.418928:0.479650:0.426402:0.479650:0.426402:0.463244:0.418928:0.463244:0.000000 z:@0.445122:0.479650:0.452356:0.479650:0.452356:0.463244:0.445122:0.463244:0.000000 y:@0.492612:0.479650:0.500086:0.479650:0.500086:0.463244:0.492612:0.463244:0.000000 z:@0.534783:0.479650:0.542017:0.479650:0.542017:0.463244:0.534783:0.463244:0.000000 x:@0.669138:0.479650:0.676593:0.479650:0.676593:0.463244:0.669138:0.463244:0.000000 La solución del sistema de ecuaciones propuesto es (1, 2, –1). :@0.293593:0.507012:0.739745:0.507012:0.739745:0.490579:0.293593:0.490579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Escribimos = {(1, 2, –1)} para referirnos al conjunto solución del sistema de ecuaciones :@0.293593:0.534374:0.931197:0.534374:0.931197:0.517941:0.293593:0.517941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.375634:0.534374:0.383697:0.534374:0.383697:0.517968:0.375634:0.517968:0.000000 propuesto.:@0.293575:0.551016:0.372041:0.551016:0.372041:0.534582:0.293575:0.534582:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La solución también la podemos expresar como = 1, = 2, = –1. :@0.293575:0.578378:0.781864:0.578378:0.781864:0.561944:0.293575:0.561944:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.646295:0.578378:0.653750:0.578378:0.653750:0.561972:0.646295:0.561972:0.000000 y:@0.688447:0.578378:0.695921:0.578378:0.695921:0.561972:0.688447:0.561972:0.000000 z:@0.730618:0.578378:0.737852:0.578378:0.737852:0.561972:0.730618:0.561972:0.000000 Ejercicio 3:@0.293575:0.605740:0.370720:0.605740:0.370720:0.589071:0.293575:0.589071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Veamos otra forma de encontrar la solución. Resolvemos el mismo sistema de ecuaciones :@0.293575:0.629524:0.931071:0.629524:0.931071:0.613090:0.293575:0.613090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lineales propuesto, pero esta vez seleccionamos la incógnita , que obtenemos de la :@0.293575:0.646166:0.930992:0.646166:0.930992:0.629732:0.293575:0.629732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.750093:0.646166:0.757566:0.646166:0.757566:0.629760:0.750093:0.629760:0.000000 tercera ecuación.:@0.293593:0.662808:0.417275:0.662808:0.417275:0.646374:0.293593:0.646374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 + – = 5:@0.374235:0.683028:0.487753:0.683028:0.487753:0.666594:0.374235:0.666594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.383144:0.683028:0.393839:0.683028:0.393839:0.666621:0.383144:0.666621:0.000000:0.000000 y:@0.420474:0.683028:0.427948:0.683028:0.427948:0.666621:0.420474:0.666621:0.000000 z:@0.452798:0.683028:0.460032:0.683028:0.460032:0.666621:0.452798:0.666621:0.000000 + 2 + 2 = 3:@0.374235:0.699669:0.486556:0.699669:0.486556:0.683236:0.374235:0.683236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.382132:0.699669:0.392827:0.699669:0.392827:0.683263:0.382132:0.683263:0.000000:0.000000 y:@0.416517:0.699669:0.423990:0.699669:0.423990:0.683263:0.416517:0.683263:0.000000 z:@0.451601:0.699669:0.458835:0.699669:0.458835:0.683263:0.451601:0.683263:0.000000 – + + = 0.:@0.374217:0.716311:0.488894:0.716311:0.488894:0.699877:0.374217:0.699877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.383347:0.716311:0.394042:0.716311:0.394042:0.699905:0.383347:0.699905:0.000000:0.000000 y:@0.416719:0.716311:0.424193:0.716311:0.424193:0.699905:0.416719:0.699905:0.000000 z:@0.450810:0.716311:0.458044:0.716311:0.458044:0.699905:0.450810:0.699905:0.000000 Tenemos y = x - z y reemplazamos en la primera y seguda ecuación: :@0.293556:0.749428:0.777634:0.749428:0.777634:0.732995:0.293556:0.732995:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 + - - = 5:@0.786245:0.742314:0.896744:0.742314:0.896744:0.725880:0.786245:0.725880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x z z:@0.795154:0.742314:0.869022:0.742314:0.869022:0.725908:0.795154:0.725908:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 + 2(:@0.786245:0.758956:0.833423:0.758956:0.833423:0.742522:0.786245:0.742522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.794142:0.758956:0.804836:0.758956:0.804836:0.742550:0.794142:0.742550:0.000000:0.000000 x-z:@0.833312:0.758956:0.853339:0.758956:0.853339:0.742550:0.833312:0.742550:0.000000:0.000000:0.000000 ) + 2 = 3:@0.853284:0.758956:0.920728:0.758956:0.920728:0.742522:0.853284:0.742522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.885773:0.758956:0.893007:0.758956:0.893007:0.742550:0.885773:0.742550:0.000000 Donde: :@0.293660:0.785229:0.355023:0.785229:0.355023:0.768795:0.293660:0.768795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3 - 2 = 5:@0.364386:0.779012:0.437150:0.779012:0.437150:0.762578:0.364386:0.762578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x z:@0.373295:0.779012:0.409428:0.779012:0.409428:0.762606:0.373295:0.762606:0.000000:0.000000:0.000000:0.000000 3 = 3:@0.364386:0.795654:0.407772:0.795654:0.407772:0.779220:0.364386:0.779220:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.373295:0.795654:0.383990:0.795654:0.383990:0.779248:0.373295:0.779248:0.000000:0.000000 De la ecuación 3 = 3 obtenemos = 1. De la primera ecuación obtenemos :@0.293660:0.816166:0.847237:0.816166:0.847237:0.799732:0.293660:0.799732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.413635:0.816166:0.421090:0.816166:0.421090:0.799760:0.413635:0.799760:0.000000 x:@0.540866:0.816166:0.548321:0.816166:0.548321:0.799760:0.540866:0.799760:0.000000 z:@0.293657:0.837870:0.300891:0.837870:0.300891:0.821464:0.293657:0.821464:0.000000 = (3 -5) con lo que = (3 1 -5) = 1).:@0.300817:0.837870:0.603076:0.837387:0.603076:0.820953:0.300817:0.821436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.322650:0.830923:0.330816:0.830923:0.330816:0.815983:0.322650:0.815983:0.000000 2:@0.322650:0.847313:0.330816:0.847313:0.330816:0.832373:0.322650:0.832373:0.000000 x:@0.351420:0.837866:0.358875:0.837866:0.358875:0.821460:0.351420:0.821460:0.000000 z:@0.466245:0.837394:0.473479:0.837394:0.473479:0.820988:0.466245:0.820988:0.000000 1:@0.495248:0.830444:0.503414:0.830444:0.503414:0.815504:0.495248:0.815504:0.000000 2:@0.495248:0.846834:0.503414:0.846834:0.503414:0.831894:0.495248:0.831894:0.000000 x:@0.524017:0.837387:0.531472:0.837387:0.531472:0.820981:0.524017:0.820981:0.000000 Como = - , entonces y = 1 - (-1) = 2:@0.293650:0.868535:0.575644:0.868535:0.575644:0.852101:0.293650:0.852101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.342319:0.868535:0.349792:0.868535:0.349792:0.852129:0.342319:0.852129:0.000000 x z:@0.368512:0.868535:0.396436:0.868535:0.396436:0.852129:0.368512:0.852129:0.000000:0.000000:0.000000 Así, la solución es (1, 2, -1), que es exactamente la misma que ya obtuvimos.:@0.293632:0.895897:0.840279:0.895897:0.840279:0.879463:0.293632:0.879463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.767386:0.332311:0.775552:0.332311:0.775552:0.317371:0.767386:0.317371:0.000000 3:@0.767386:0.348701:0.775552:0.348701:0.775552:0.333761:0.767386:0.333761:0.000000 1:@0.795201:0.332311:0.803367:0.332311:0.803367:0.317371:0.795201:0.317371:0.000000 2:@0.795201:0.348701:0.803367:0.348701:0.803367:0.333761:0.795201:0.333761:0.000000 1:@0.871834:0.332311:0.880000:0.332311:0.880000:0.317371:0.871834:0.317371:0.000000 3:@0.871834:0.348701:0.880000:0.348701:0.880000:0.333761:0.871834:0.333761:0.000000 5:@0.822201:0.332311:0.830367:0.332311:0.830367:0.317371:0.822201:0.317371:0.000000 2:@0.822201:0.348701:0.830367:0.348701:0.830367:0.333761:0.822201:0.333761:0.000000 5:@0.901483:0.332311:0.909649:0.332311:0.909649:0.317371:0.901483:0.317371:0.000000 3:@0.901483:0.348701:0.909649:0.348701:0.909649:0.333761:0.901483:0.333761:0.000000 1:@0.500884:0.443635:0.509050:0.443635:0.509050:0.428695:0.500884:0.428695:0.000000 3:@0.500884:0.460024:0.509050:0.460024:0.509050:0.445085:0.500884:0.445085:0.000000 1:@0.759180:0.443813:0.767346:0.443813:0.767346:0.428873:0.759180:0.428873:0.000000 3:@0.759180:0.460202:0.767346:0.460202:0.767346:0.445262:0.759180:0.445262:0.000000 1:@0.699886:0.472402:0.708053:0.472402:0.708053:0.457463:0.699886:0.457463:0.000000 2:@0.699886:0.488792:0.708053:0.488792:0.708053:0.473852:0.699886:0.473852:0.000000 3:@0.529121:0.443635:0.537287:0.443635:0.537287:0.428695:0.529121:0.428695:0.000000 5:@0.529121:0.460024:0.537287:0.460024:0.537287:0.445085:0.529121:0.445085:0.000000 5:@0.790974:0.443813:0.799140:0.443813:0.799140:0.428873:0.790974:0.428873:0.000000 3:@0.790974:0.460202:0.799140:0.460202:0.799140:0.445262:0.790974:0.445262:0.000000 3:@0.608138:0.366441:0.616304:0.366441:0.616304:0.351501:0.608138:0.351501:0.000000 2:@0.608138:0.382830:0.616304:0.382830:0.616304:0.367890:0.608138:0.367890:0.000000 1:@0.634280:0.366441:0.642446:0.366441:0.642446:0.351501:0.634280:0.351501:0.000000 3:@0.634280:0.382830:0.642446:0.382830:0.642446:0.367890:0.634280:0.367890:0.000000 1:@0.717606:0.366441:0.725772:0.366441:0.725772:0.351501:0.717606:0.351501:0.000000 2:@0.717606:0.382830:0.725772:0.382830:0.725772:0.367890:0.717606:0.367890:0.000000 5:@0.669369:0.366441:0.677535:0.366441:0.677535:0.351501:0.669369:0.351501:0.000000 3:@0.669369:0.382830:0.677535:0.382830:0.677535:0.367890:0.669369:0.367890:0.000000 5:@0.762737:0.366441:0.770903:0.366441:0.770903:0.351501:0.762737:0.351501:0.000000 2:@0.762737:0.382830:0.770903:0.382830:0.770903:0.367890:0.762737:0.367890:0.000000 1:@0.633003:0.396639:0.641169:0.396639:0.641169:0.381699:0.633003:0.381699:0.000000 2:@0.633003:0.413029:0.641169:0.413029:0.641169:0.398089:0.633003:0.398089:0.000000 5:@0.667446:0.396639:0.675612:0.396639:0.675612:0.381699:0.667446:0.381699:0.000000 2:@0.667446:0.413029:0.675612:0.413029:0.675612:0.398089:0.667446:0.398089:0.000000 1:@0.711230:0.396639:0.719396:0.396639:0.719396:0.381699:0.711230:0.381699:0.000000 2:@0.711230:0.413029:0.719396:0.413029:0.719396:0.398089:0.711230:0.398089:0.000000 5:@0.755741:0.396639:0.763907:0.396639:0.763907:0.381699:0.755741:0.381699:0.000000 2:@0.755741:0.413029:0.763907:0.413029:0.763907:0.398089:0.755741:0.398089:0.000000 1:@0.372587:0.473296:0.380753:0.473296:0.380753:0.458356:0.372587:0.458356:0.000000 2:@0.372587:0.489686:0.380753:0.489686:0.380753:0.474746:0.372587:0.474746:0.000000 En el ejercicio resuelto 1, :@0.078581:0.187395:0.243525:0.187395:0.243525:0.172455:0.078581:0.172455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el reemplazo de de :@0.078580:0.202524:0.218994:0.202524:0.218994:0.187584:0.078580:0.187584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.187869:0.202524:0.194646:0.202524:0.194646:0.187609:0.187869:0.187609:0.000000 la primera ecuación en :@0.078580:0.217652:0.233094:0.217652:0.233094:0.202713:0.078580:0.202713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la segunda y tercera :@0.078580:0.232781:0.214531:0.232781:0.214531:0.217842:0.078580:0.217842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ecuaciones dio lugar al :@0.078580:0.247910:0.233734:0.247910:0.233734:0.232971:0.078580:0.232971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sistema de dos ecuaciones :@0.078580:0.263039:0.258814:0.263039:0.258814:0.248099:0.078580:0.248099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lineales con las incógnitas :@0.078580:0.278168:0.253124:0.278168:0.253124:0.263228:0.078580:0.263228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y z:@0.078580:0.293297:0.098309:0.293297:0.098309:0.278383:0.078580:0.278383:0.000000:0.000000:0.000000 , . Este sistema lo :@0.085307:0.293297:0.204867:0.293297:0.204867:0.278357:0.085307:0.278357:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 resolvemos por el método :@0.078563:0.308426:0.256173:0.308426:0.256173:0.293486:0.078563:0.293486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de sustitución.:@0.078563:0.323555:0.174348:0.323555:0.174348:0.308615:0.078563:0.308615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Este método es muy :@0.078563:0.345832:0.217409:0.345832:0.217409:0.330893:0.078563:0.330893:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 flexible en el siguiente :@0.078563:0.360961:0.229546:0.360961:0.229546:0.346022:0.078563:0.346022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sentido: la incógnita :@0.078563:0.376090:0.225486:0.376090:0.225486:0.361150:0.078563:0.361150:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.215044:0.376090:0.221822:0.376090:0.221822:0.361176:0.215044:0.361176:0.000000 fue elegida de la primera :@0.078563:0.391219:0.246107:0.391219:0.246107:0.376279:0.078563:0.376279:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ecuación; esta misma :@0.078563:0.406348:0.223964:0.406348:0.223964:0.391408:0.078563:0.391408:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 incógnita se pudo obtener :@0.078563:0.421477:0.258472:0.421477:0.258472:0.406537:0.078563:0.406537:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de la segunda o tercera :@0.078563:0.436606:0.236735:0.436606:0.236735:0.421666:0.078563:0.421666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ecuación y se reemplazó :@0.078563:0.451735:0.244936:0.451735:0.244936:0.436795:0.078563:0.436795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en las restantes, lo que dio :@0.078563:0.466864:0.256225:0.466864:0.256225:0.451924:0.078563:0.451924:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lugar a un sistema de dos :@0.078563:0.481993:0.250396:0.481993:0.250396:0.467053:0.078563:0.467053:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ecuaciones lineales con :@0.078563:0.497122:0.238304:0.497122:0.238304:0.482182:0.078563:0.482182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dos incógnitas:@0.078563:0.512251:0.174876:0.512251:0.174876:0.497311:0.078563:0.497311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , ) .:@0.135358:0.534528:0.202410:0.534527:0.202410:0.519587:0.135358:0.519588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x z:@0.139725:0.534528:0.159438:0.534528:0.159438:0.519614:0.139725:0.519614:0.000000:0.000000:0.000000 ∈:@0.167319:0.534150:0.179251:0.534150:0.179251:0.518706:0.167319:0.518706:0.000000 ℝ:@0.182765:0.535058:0.194847:0.535058:0.194847:0.519008:0.182765:0.519008:0.000000 2:@0.194781:0.529014:0.199542:0.529014:0.199542:0.520304:0.194781:0.520304:0.000000 Competencia :@0.078581:0.146688:0.187141:0.146688:0.187141:0.129741:0.078581:0.129741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.078581:0.163330:0.176057:0.163330:0.176057:0.146383:0.078581:0.146383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (Ev.) Resuelve sistemas de ecuaciones de tres incógnitas por sustitución:@0.542123:0.972377:0.917828:0.972377:0.917828:0.960425:0.542123:0.960425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000