14:@0.058194:0.966765:0.075166:0.966765:0.075166:0.950778:0.058194:0.950778:0.000000:0.000000
Tenemos   =   –   y reemplazamos en la primera y segunda ecuación: :@0.404235:0.106886:0.895878:0.106886:0.895878:0.090389:0.404235:0.090389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y x z:@0.472626:0.107002:0.530615:0.107002:0.530615:0.090533:0.472626:0.090533:0.000000:0.000000:0.000000:0.000000:0.000000
2  +   –   –   = 5:@0.584692:0.133288:0.705678:0.133288:0.705678:0.116791:0.584692:0.116791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x z z:@0.593188:0.133404:0.678090:0.133404:0.678090:0.116935:0.593188:0.116935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.584692:0.150755:0.592167:0.150755:0.592167:0.134286:0.584692:0.134286:0.000000
 + 2(  –  ) + 2  = 3,:@0.592167:0.150639:0.729143:0.150639:0.729143:0.134141:0.592167:0.134141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x z:@0.625708:0.150755:0.658613:0.150755:0.658613:0.134286:0.625708:0.134286:0.000000:0.000000:0.000000
z:@0.692154:0.150755:0.698800:0.150755:0.698800:0.134286:0.692154:0.134286:0.000000
donde::@0.404235:0.175118:0.453881:0.175118:0.453881:0.158620:0.404235:0.158620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3  – 2  = 5:@0.609255:0.192469:0.686740:0.192469:0.686740:0.175971:0.609255:0.175971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.617751:0.192585:0.625226:0.192585:0.625226:0.176116:0.617751:0.176116:0.000000
z:@0.652506:0.192585:0.659152:0.192585:0.659152:0.176116:0.652506:0.176116:0.000000
         3  = 3.:@0.607945:0.209820:0.688070:0.209820:0.688070:0.193322:0.607945:0.193322:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.650252:0.209935:0.657727:0.209935:0.657727:0.193467:0.650252:0.193467:0.000000
De la ecuación 3  = 3 obtenemos   = 1. De la primera ecuación :@0.404235:0.244521:0.895901:0.244521:0.895901:0.228023:0.404235:0.228023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.530653:0.244637:0.538128:0.244637:0.538128:0.228168:0.530653:0.228168:0.000000
x:@0.667205:0.244637:0.674680:0.244637:0.674680:0.228168:0.667205:0.228168:0.000000
obtenemos    =      (3  – 5), con lo que   =      (3 × 1 – 5) = –1.:@0.404235:0.269000:0.844677:0.269000:0.844677:0.252503:0.404235:0.252503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
z:@0.493781:0.269116:0.500428:0.269116:0.500428:0.252647:0.493781:0.252647:0.000000
x:@0.554679:0.269116:0.562154:0.269116:0.562154:0.252647:0.554679:0.252647:0.000000
z:@0.682117:0.269116:0.688763:0.269116:0.688763:0.252647:0.682117:0.252647:0.000000
 :@0.404235:0.286351:0.408377:0.286351:0.408377:0.269853:0.404235:0.269853:0.000000
Como   =   –  , entonces   = 1 – (–1) = 2.:@0.404235:0.303702:0.704115:0.303702:0.704115:0.287204:0.404235:0.287204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y x z:@0.453380:0.303817:0.513064:0.303817:0.513064:0.287349:0.453380:0.287349:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.588813:0.303817:0.596500:0.303817:0.596500:0.287349:0.588813:0.287349:0.000000
Así, la solución es (1, 2, –1), que es exactamente la misma que ya :@0.404235:0.338403:0.895847:0.338403:0.895847:0.321906:0.404235:0.321906:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
obtuvimos.:@0.404235:0.355754:0.483935:0.355754:0.483935:0.339256:0.404235:0.339256:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicio resuelto:@0.404235:0.390831:0.522213:0.390831:0.522213:0.374045:0.404235:0.374045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Consideremos el sistema de ecuaciones lineales definido por: :@0.404235:0.407806:0.839587:0.407806:0.839587:0.391309:0.404235:0.391309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ,  ) :@0.404235:0.425157:0.455480:0.425157:0.455480:0.408659:0.404235:0.408659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.410187:0.425273:0.445443:0.425273:0.445443:0.408804:0.410187:0.408804:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.455422:0.424940:0.471470:0.424940:0.471470:0.410293:0.455422:0.410293:0.000000
 :@0.471410:0.424640:0.475807:0.424640:0.475807:0.411266:0.471410:0.411266:0.000000
:@0.475754:0.424189:0.489663:0.424189:0.489663:0.410743:0.475754:0.410743:0.000000
3:@0.489606:0.418805:0.494560:0.418805:0.494560:0.409187:0.489606:0.409187:0.000000
, y :@0.494525:0.425158:0.513386:0.425158:0.513386:0.408661:0.494525:0.408661:0.000000:0.000000:0.000000:0.000000
     x:@0.584686:0.442625:0.610945:0.442625:0.610945:0.426156:0.584686:0.426156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
         +   = 4:@0.610945:0.442509:0.699141:0.442509:0.699141:0.426011:0.610945:0.426011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
z:@0.664907:0.442625:0.671553:0.442625:0.671553:0.426156:0.664907:0.426156:0.000000
–2  +   –     = 0:@0.584686:0.459860:0.699238:0.459860:0.699238:0.443362:0.584686:0.443362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.603682:0.459975:0.637935:0.459975:0.637935:0.443507:0.603682:0.443507:0.000000:0.000000:0.000000
z:@0.665003:0.459975:0.671650:0.459975:0.671650:0.443507:0.665003:0.443507:0.000000
   3  –   + 2  = 4.:@0.584686:0.477210:0.701819:0.477210:0.701819:0.460713:0.584686:0.460713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.603297:0.477326:0.637242:0.477326:0.637242:0.460857:0.603297:0.460857:0.000000:0.000000:0.000000
z:@0.664830:0.477326:0.671476:0.477326:0.671476:0.460857:0.664830:0.460857:0.000000
Aplicamos el método de sustitución.  :@0.404229:0.508398:0.672671:0.508398:0.672671:0.491901:0.404229:0.491901:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De la tercera ecuación obtenemos   = 3  + 2  – 4. Reemplazamos en :@0.404229:0.525749:0.895934:0.525749:0.895934:0.509252:0.404229:0.509252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.651092:0.525865:0.658778:0.525865:0.658778:0.509396:0.651092:0.509396:0.000000
x:@0.686251:0.525865:0.693726:0.525865:0.693726:0.509396:0.686251:0.509396:0.000000
z:@0.721198:0.525865:0.727844:0.525865:0.727844:0.509396:0.721198:0.509396:0.000000
la segunda ecuación:  :@0.404229:0.543100:0.559235:0.543100:0.559235:0.526602:0.404229:0.526602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–2  + (–4 + 3  + 2 ) –   = 0:@0.548602:0.567579:0.747381:0.567579:0.747381:0.551081:0.548602:0.551081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.567598:0.567695:0.575073:0.567695:0.575073:0.551226:0.567598:0.551226:0.000000
x:@0.646701:0.567695:0.654176:0.567695:0.654176:0.551226:0.646701:0.551226:0.000000
z:@0.681764:0.567695:0.688410:0.567695:0.688410:0.551226:0.681764:0.551226:0.000000
z:@0.713147:0.567695:0.719794:0.567695:0.719794:0.551226:0.713147:0.551226:0.000000
y, luego de simplificar, resulta::@0.404229:0.602280:0.612636:0.602280:0.612636:0.585783:0.404229:0.585783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x z:@0.616224:0.626875:0.649437:0.626875:0.649437:0.610406:0.616224:0.610406:0.000000:0.000000:0.000000
 +   = 4,:@0.623698:0.626760:0.679780:0.626760:0.679780:0.610262:0.623698:0.610262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que es exactamente la primera ecuación.:@0.404229:0.657947:0.693261:0.657947:0.693261:0.641450:0.404229:0.641450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Como se puede observar, este sistema es :@0.404229:0.690379:0.696404:0.690379:0.696404:0.673881:0.404229:0.673881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sobredeterminado:@0.696423:0.690596:0.833611:0.690596:0.833611:0.673881:0.696423:0.673881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, esto es, :@0.833613:0.690379:0.895917:0.690379:0.895917:0.673881:0.833613:0.673881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
admite una :@0.404229:0.707730:0.489612:0.707730:0.489612:0.691232:0.404229:0.691232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
infinidad de soluciones:@0.489612:0.707947:0.659933:0.707947:0.659933:0.691232:0.489612:0.691232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.659936:0.707730:0.662691:0.707730:0.662691:0.691232:0.659936:0.691232:0.000000
El par de ecuaciones se reduce a una sola ecuación   +   = 4, donde: :@0.404229:0.742431:0.889359:0.742431:0.889359:0.725934:0.404229:0.725934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x z:@0.767874:0.742547:0.801087:0.742547:0.801087:0.726078:0.767874:0.726078:0.000000:0.000000:0.000000
z:@0.581642:0.759898:0.588289:0.759898:0.588289:0.743429:0.581642:0.743429:0.000000
 = 4 –         :@0.588289:0.759782:0.677429:0.759782:0.677429:0.743284:0.588289:0.743284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x,:@0.634660:0.759898:0.645102:0.759898:0.645102:0.743429:0.634660:0.743429:0.000000:0.000000
x:@0.665812:0.759898:0.673287:0.759898:0.673287:0.743429:0.665812:0.743429:0.000000
:@0.677429:0.759565:0.693477:0.759565:0.693477:0.744918:0.677429:0.744918:0.000000
 :@0.693413:0.759256:0.697810:0.759256:0.697810:0.745883:0.693413:0.745883:0.000000
:@0.697758:0.758806:0.711668:0.758806:0.711668:0.745359:0.697758:0.745359:0.000000
.:@0.711610:0.759775:0.714365:0.759775:0.714365:0.743277:0.711610:0.743277:0.000000
Asignando un valor de   :@0.404233:0.794477:0.578947:0.794477:0.578947:0.777979:0.404233:0.777979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.567330:0.794592:0.574805:0.794592:0.574805:0.778123:0.567330:0.778123:0.000000
:@0.578371:0.794260:0.594419:0.794260:0.594419:0.779613:0.578371:0.779613:0.000000
 :@0.594361:0.793958:0.598758:0.793958:0.598758:0.780585:0.594361:0.780585:0.000000
:@0.598093:0.793508:0.612003:0.793508:0.612003:0.780061:0.598093:0.780061:0.000000
, podemos calcular  y, en consecuencia, :@0.611945:0.794477:0.895909:0.794477:0.895909:0.777979:0.611945:0.777979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
z :@0.748013:0.794592:0.758802:0.794592:0.758802:0.778123:0.748013:0.778123:0.000000:0.000000
el valor de  . Puesto que   = –4 + 3  + 2 , se sigue que: :@0.404246:0.811827:0.793921:0.811827:0.793921:0.795330:0.404246:0.795330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.481363:0.811943:0.489050:0.811943:0.489050:0.795474:0.481363:0.795474:0.000000
y:@0.579346:0.811943:0.587033:0.811943:0.587033:0.795474:0.579346:0.795474:0.000000
x:@0.652708:0.811943:0.660183:0.811943:0.660183:0.795474:0.652708:0.795474:0.000000
z:@0.687771:0.811943:0.694418:0.811943:0.694418:0.795474:0.687771:0.795474:0.000000
y:@0.505273:0.836422:0.512960:0.836422:0.512960:0.819953:0.505273:0.819953:0.000000
 = –4 + 3  + 2(4 –  ) = 4 +          :@0.512960:0.836306:0.753834:0.836306:0.753834:0.819809:0.512960:0.819809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.578635:0.836422:0.586110:0.836422:0.586110:0.819953:0.578635:0.819953:0.000000
x:@0.646931:0.836422:0.654406:0.836422:0.654406:0.819953:0.646931:0.819953:0.000000
x ,:@0.707038:0.836422:0.721506:0.836422:0.721506:0.819953:0.707038:0.819953:0.000000:0.000000:0.000000
x:@0.742217:0.836422:0.749692:0.836422:0.749692:0.819953:0.742217:0.819953:0.000000
:@0.753834:0.836089:0.769882:0.836089:0.769882:0.821443:0.753834:0.821443:0.000000
 :@0.769799:0.835787:0.774196:0.835787:0.774196:0.822414:0.769799:0.822414:0.000000
:@0.774143:0.835337:0.788052:0.835337:0.788052:0.821890:0.774143:0.821890:0.000000
.:@0.787994:0.836306:0.790749:0.836306:0.790749:0.819808:0.787994:0.819808:0.000000
Así, las soluciones del sistema de ecuaciones propuesto tienen la forma::@0.404230:0.871007:0.891728:0.871007:0.891728:0.854510:0.404230:0.854510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.584688:0.895602:0.596305:0.895602:0.596305:0.879133:0.584688:0.879133:0.000000:0.000000
:@0.596305:0.895269:0.612353:0.895269:0.612353:0.880622:0.596305:0.880622:0.000000
 :@0.612291:0.894967:0.616688:0.894967:0.616688:0.881594:0.612291:0.881594:0.000000
:@0.616636:0.894517:0.630546:0.894517:0.630546:0.881070:0.616636:0.881070:0.000000
    dado,:@0.630488:0.895486:0.687340:0.895486:0.687340:0.878988:0.630488:0.878988:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.584695:0.912952:0.592382:0.912952:0.592382:0.896483:0.584695:0.896483:0.000000
 = 4 + :@0.592382:0.912836:0.639061:0.912836:0.639061:0.896339:0.592382:0.896339:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x,:@0.639061:0.912952:0.649503:0.912952:0.649503:0.896483:0.639061:0.896483:0.000000:0.000000
z:@0.584695:0.930303:0.591341:0.930303:0.591341:0.913834:0.584695:0.913834:0.000000
 = 4 – :@0.591341:0.930187:0.637713:0.930187:0.637713:0.913689:0.591341:0.913689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x.:@0.637713:0.930303:0.648154:0.930303:0.648154:0.913834:0.637713:0.913834:0.000000:0.000000
Competencia digital:@0.199646:0.526521:0.341998:0.526521:0.341998:0.511048:0.199646:0.511048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para reforzar y ampliar la :@0.199884:0.555148:0.363117:0.555148:0.363117:0.540085:0.199884:0.540085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resolución de sistemas de ecua-:@0.153341:0.570990:0.357927:0.570990:0.357927:0.555927:0.153341:0.555927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciones lineales con tres ecuacio-:@0.153341:0.586832:0.359863:0.586832:0.359863:0.571769:0.153341:0.571769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nes y tres incógnitas, :@0.153341:0.602674:0.290576:0.602674:0.290576:0.587611:0.153341:0.587611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
observa:@0.290576:0.603096:0.345614:0.603096:0.345614:0.587624:0.290576:0.587624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 el :@0.345617:0.602674:0.363858:0.602674:0.363858:0.587611:0.345617:0.587611:0.000000:0.000000:0.000000:0.000000
siguiente video: :@0.153341:0.618516:0.256928:0.618516:0.256928:0.603453:0.153341:0.603453:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lynk.ec/12m01:@0.256928:0.618846:0.354817:0.618846:0.354817:0.603532:0.256928:0.603532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.524244:0.260139:0.532740:0.260139:0.532740:0.243641:0.524244:0.243641:0.000000
2:@0.524244:0.276477:0.532740:0.276477:0.532740:0.259980:0.524244:0.259980:0.000000
1:@0.710988:0.260139:0.719484:0.260139:0.719484:0.243641:0.710988:0.243641:0.000000
2:@0.710988:0.276477:0.719484:0.276477:0.719484:0.259980:0.710988:0.259980:0.000000
Competencia :@0.199644:0.141277:0.297267:0.141277:0.297267:0.125805:0.199644:0.125805:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.199644:0.153845:0.283707:0.153845:0.283707:0.138373:0.199644:0.138373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Al ser el método de sus-:@0.199880:0.178320:0.356572:0.178320:0.356572:0.163257:0.199880:0.163257:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
titución muy flexible también :@0.153337:0.194162:0.349761:0.194162:0.349761:0.179099:0.153337:0.179099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se pudo haber seleccionado la :@0.153337:0.210004:0.352945:0.210004:0.352945:0.194941:0.153337:0.194941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
incógnita   de cualquiera de las :@0.153337:0.225846:0.359052:0.225846:0.359052:0.210783:0.153337:0.210783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
z:@0.218016:0.225951:0.224084:0.225951:0.224084:0.210915:0.218016:0.210915:0.000000
tres ecuaciones. Al reemplazar :@0.153337:0.241688:0.353086:0.241688:0.353086:0.226625:0.153337:0.226625:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ese resultado en las otras dos :@0.153337:0.257530:0.345821:0.257530:0.345821:0.242467:0.153337:0.242467:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuaciones restantes, se obtiene :@0.153337:0.273372:0.364256:0.273372:0.364256:0.258309:0.153337:0.258309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un sistema de dos ecuaciones :@0.153337:0.289214:0.349234:0.289214:0.349234:0.274151:0.153337:0.274151:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lineales con dos incógnitas:@0.153337:0.305056:0.326296:0.305056:0.326296:0.289993:0.153337:0.289993:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ) :@0.220971:0.328027:0.255764:0.328027:0.255764:0.312964:0.220971:0.312964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.226406:0.328132:0.246547:0.328132:0.246547:0.313096:0.226406:0.313096:0.000000:0.000000:0.000000
:@0.255771:0.327677:0.269726:0.327677:0.269726:0.314940:0.255771:0.314940:0.000000
 :@0.269726:0.327827:0.274124:0.327827:0.274124:0.314454:0.269726:0.314454:0.000000
:@0.274124:0.327141:0.286824:0.327141:0.286824:0.314863:0.274124:0.314863:0.000000
2:@0.286822:0.322226:0.291344:0.322226:0.291344:0.313444:0.286822:0.313444:0.000000
.:@0.291345:0.328025:0.293860:0.328025:0.293860:0.312962:0.291345:0.312962:0.000000
Resume:@0.153351:0.344290:0.208479:0.344290:0.208479:0.328818:0.153351:0.328818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en el cuaderno cómo :@0.208479:0.343867:0.354157:0.343867:0.354157:0.328804:0.208479:0.328804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resolver un sistemas de tres :@0.153351:0.359709:0.333700:0.359709:0.333700:0.344646:0.153351:0.344646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuaciones lineales con tres :@0.153351:0.375551:0.335424:0.375551:0.335424:0.360488:0.153351:0.360488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
incógnitas utilizando el método :@0.153351:0.391393:0.363443:0.391393:0.363443:0.376330:0.153351:0.376330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de sustitución.:@0.153351:0.407235:0.246858:0.407235:0.246858:0.392172:0.153351:0.392172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.199646:0.833755:0.297269:0.833755:0.297269:0.818282:0.199646:0.818282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicacional:@0.199646:0.846323:0.311604:0.846323:0.311604:0.830850:0.199646:0.830850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El término ecuación se :@0.193074:0.870797:0.343785:0.870797:0.343785:0.855734:0.193074:0.855734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
origina en el latín :@0.153338:0.886639:0.267656:0.886639:0.267656:0.871576:0.153338:0.871576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aequatio, :@0.267656:0.886745:0.329484:0.886745:0.329484:0.871708:0.267656:0.871708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que significa “nivelar, igualar o :@0.153338:0.902481:0.348937:0.902481:0.348937:0.887418:0.153338:0.887418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
repartir igual”.:@0.153338:0.918323:0.241482:0.918323:0.241482:0.903260:0.153338:0.903260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000