60:@0.058783:0.510692:0.077690:0.510692:0.077690:0.494068:0.058783:0.494068:0.000000:0.000000
Tema:@0.047190:0.135475:0.083321:0.135475:0.083321:0.113749:0.047190:0.113749:0.000000:0.000000:0.000000:0.000000
b) :@0.540845:0.624344:0.560876:0.624344:0.560876:0.607444:0.540845:0.607444:0.000000:0.000000:0.000000
¿Están alineados los puntos?:@0.574089:0.624344:0.782319:0.624344:0.782319:0.607955:0.574089:0.607955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
__________________________________________:@0.574085:0.648654:0.878342:0.648654:0.878342:0.635245:0.574085:0.635245:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c) :@0.540845:0.675980:0.558481:0.675980:0.558481:0.659080:0.540845:0.659080:0.000000:0.000000:0.000000
Escribe:@0.574089:0.675980:0.628837:0.675980:0.628837:0.659356:0.574089:0.659356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 dos puntos diferentes que son la :@0.628837:0.675980:0.884963:0.675980:0.884963:0.659591:0.628837:0.659591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.880890:0.675980:0.884926:0.675980:0.884926:0.659591:0.880890:0.659591:0.000000
solución de la ecuación lineal.:@0.574089:0.692577:0.792489:0.692577:0.792489:0.676188:0.574089:0.676188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
__________________________________________:@0.574085:0.716887:0.878342:0.716887:0.878342:0.703478:0.574085:0.703478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d) :@0.540845:0.744214:0.560913:0.744214:0.560913:0.727313:0.540845:0.727313:0.000000:0.000000:0.000000
Determina:@0.574089:0.744214:0.655778:0.744214:0.655778:0.727590:0.574089:0.727590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 si los siguientes puntos son :@0.655778:0.744214:0.884904:0.744214:0.884904:0.727825:0.655778:0.727825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
soluciones de la ecuación lineal.:@0.574089:0.760810:0.808300:0.760810:0.808300:0.744422:0.574089:0.744422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.540845:0.785746:0.544660:0.785746:0.544660:0.768846:0.540845:0.768846:0.000000
i)    :@0.574089:0.785746:0.598671:0.785746:0.598671:0.768846:0.574089:0.768846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
_______________________________________:@0.598340:0.785119:0.880885:0.785119:0.880885:0.771710:0.598340:0.771710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.540845:0.810686:0.544660:0.810686:0.544660:0.793786:0.540845:0.793786:0.000000
ii)   :@0.574089:0.810686:0.599077:0.810686:0.599077:0.793786:0.574089:0.793786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
_______________________________________:@0.598340:0.810058:0.880885:0.810058:0.880885:0.796649:0.598340:0.796649:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.540845:0.835625:0.544660:0.835625:0.544660:0.818724:0.540845:0.818724:0.000000
iii)  :@0.574089:0.835625:0.601417:0.835625:0.601417:0.818724:0.574089:0.818724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
______________________________________:@0.601414:0.834996:0.876722:0.834996:0.876722:0.821587:0.601414:0.821587:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.540845:0.860562:0.544660:0.860562:0.544660:0.843662:0.540845:0.843662:0.000000
iv)  :@0.574089:0.860562:0.601343:0.860562:0.601343:0.843662:0.574089:0.843662:0.000000:0.000000:0.000000:0.000000:0.000000
______________________________________:@0.601340:0.859934:0.876649:0.859934:0.876649:0.846524:0.601340:0.846524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e) :@0.540845:0.890824:0.559715:0.890824:0.559715:0.873924:0.540845:0.873924:0.000000:0.000000:0.000000
¿Cuál es la pendiente de esta función lineal?:@0.574089:0.890824:0.880927:0.890824:0.880927:0.874435:0.574089:0.874435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
__________________________________________:@0.574085:0.915134:0.878342:0.915134:0.878342:0.901725:0.574085:0.901725:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.115209:0.624344:0.133950:0.624344:0.133950:0.607208:0.115209:0.607208:0.000000:0.000000:0.000000
Completa:@0.148452:0.624344:0.223471:0.624344:0.223471:0.607720:0.148452:0.607720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la siguiente tabla de valores con  :@0.223471:0.624344:0.491538:0.624344:0.491538:0.607955:0.223471:0.607955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
soluciones de la ecuación   –   = 3.:@0.148452:0.640941:0.404302:0.640941:0.404302:0.624552:0.148452:0.624552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.340818:0.640941:0.373048:0.640941:0.373048:0.624579:0.340818:0.624579:0.000000:0.000000:0.000000
 :@0.115209:0.701365:0.118931:0.701365:0.118931:0.684229:0.115209:0.684229:0.000000
x:@0.173175:0.668024:0.180932:0.668024:0.180932:0.652911:0.173175:0.652911:0.000000
–3:@0.225141:0.668024:0.241693:0.668024:0.241693:0.653125:0.225141:0.653125:0.000000:0.000000
–1:@0.337885:0.668024:0.354436:0.668024:0.354436:0.653125:0.337885:0.653125:0.000000:0.000000
0:@0.398445:0.668024:0.406620:0.668024:0.406620:0.653125:0.398445:0.653125:0.000000
1:@0.454817:0.668024:0.462992:0.668024:0.462992:0.653125:0.454817:0.653125:0.000000
y:@0.173108:0.692969:0.180999:0.692969:0.180999:0.677856:0.173108:0.677856:0.000000
–5:@0.281513:0.692969:0.298065:0.692969:0.298065:0.678070:0.281513:0.678070:0.000000:0.000000
a) :@0.148451:0.725084:0.167173:0.725084:0.167173:0.708184:0.148451:0.708184:0.000000:0.000000:0.000000
Construye:@0.181694:0.725084:0.259827:0.725084:0.259827:0.708460:0.181694:0.708460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 un gráfico con esos puntos.:@0.259827:0.725084:0.465771:0.725084:0.465771:0.708695:0.259827:0.708695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Taller:@0.175844:0.582740:0.236739:0.582740:0.236739:0.548793:0.175844:0.548793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
I.M.4.3.5. Plantea y resuelve problemas que involucren sistemas de dos ecuaciones lineales con dos incógnitas, ecuaciones de segundo :@0.256865:0.560206:0.877677:0.560206:0.877677:0.549776:0.256865:0.549776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
grado y la aplicación de las propiedades de las raíces de la ecuación de segundo grado; juzga la validez de las soluciones obtenidas :@0.256865:0.570767:0.877758:0.570767:0.877758:0.560338:0.256865:0.560338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en el contexto del problema.:@0.256865:0.581328:0.391462:0.581328:0.391462:0.570899:0.256865:0.570899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Gráficamente el conjunto solución de la ecuación :@0.507603:0.447808:0.883247:0.447808:0.883247:0.431419:0.507603:0.431419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lineal con dos incógnitas   +   = 15 está formado :@0.507603:0.464404:0.883249:0.464404:0.883249:0.448015:0.507603:0.448015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.698901:0.464404:0.706364:0.464404:0.706364:0.448043:0.698901:0.448043:0.000000
y:@0.728127:0.464404:0.735609:0.464404:0.735609:0.448043:0.728127:0.448043:0.000000
por todos los puntos de la recta mostrada.:@0.507603:0.481001:0.816779:0.481001:0.816779:0.464612:0.507603:0.464612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En ocasiones solo importan las soluciones enteras :@0.507603:0.504720:0.883251:0.504720:0.883251:0.488331:0.507603:0.488331:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la ecuación en determinado intervalo.:@0.507603:0.521316:0.808466:0.521316:0.808466:0.504927:0.507603:0.504927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una ecuación lineal es una expresión de la forma   +   =  , donde  ,   y   son números reales y el grado :@0.115205:0.167758:0.883877:0.167758:0.883877:0.151369:0.115205:0.151369:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax by c:@0.473769:0.167758:0.551424:0.167758:0.551424:0.151397:0.473769:0.151397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.610596:0.167758:0.659079:0.167758:0.659079:0.151397:0.610596:0.151397:0.000000:0.000000:0.000000:0.000000:0.000000
de la incógnita   e   es 1.:@0.115187:0.184354:0.295979:0.184354:0.295979:0.167965:0.115187:0.167965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.227944:0.184354:0.259897:0.184354:0.259897:0.167993:0.227944:0.167993:0.000000:0.000000:0.000000
Las ecuaciones lineales con dos incógnitas también son conocidas como ecuaciones indeterminadas, :@0.115187:0.208073:0.883942:0.208073:0.883942:0.191684:0.115187:0.191684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ya que tienen una infinidad de soluciones que son pares de números que verifican la ecuación; todos :@0.115187:0.224670:0.883837:0.224670:0.883837:0.208281:0.115187:0.208281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ubicados sobre una misma recta.:@0.115187:0.241266:0.356604:0.241266:0.356604:0.224877:0.115187:0.224877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Actividad resuelta:@0.115209:0.273946:0.272331:0.273946:0.272331:0.255509:0.115209:0.255509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Construyamos:@0.115209:0.293791:0.225885:0.293791:0.225885:0.277167:0.115209:0.277167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 una tabla de valores que satisfacen la siguiente ecuación lineal:   +   = 15:@0.225885:0.293791:0.765959:0.293791:0.765959:0.277402:0.225885:0.277402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.694920:0.293791:0.702383:0.293791:0.702383:0.277430:0.694920:0.277430:0.000000
y:@0.721438:0.293791:0.728919:0.293791:0.728919:0.277430:0.721438:0.277430:0.000000
Primero, :@0.115209:0.317510:0.179466:0.317510:0.179466:0.301121:0.115209:0.301121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
despejamos:@0.179466:0.317510:0.272249:0.317510:0.272249:0.300886:0.179466:0.300886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la variable  :   = 15 – :@0.272249:0.317510:0.430653:0.317510:0.430653:0.301121:0.272249:0.301121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y y:@0.354123:0.317510:0.376329:0.317510:0.376329:0.301149:0.354123:0.301149:0.000000:0.000000:0.000000
x:@0.430653:0.317510:0.438116:0.317510:0.438116:0.301149:0.430653:0.301149:0.000000
Luego, :@0.115209:0.341229:0.168612:0.341229:0.168612:0.324840:0.115209:0.324840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
asignamos:@0.168852:0.341229:0.251426:0.341229:0.251426:0.324605:0.168852:0.324605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 valores arbitrarios a   , :@0.251426:0.341229:0.420885:0.341229:0.420885:0.324840:0.251426:0.324840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.401904:0.341229:0.409367:0.341229:0.409367:0.324868:0.401904:0.324868:0.000000
efectuamos :@0.421124:0.341229:0.515050:0.341229:0.515050:0.324605:0.421124:0.324605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las operaciones   :@0.515273:0.341229:0.644764:0.341229:0.644764:0.324840:0.515273:0.324840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.633247:0.341229:0.640728:0.341229:0.640728:0.324868:0.633247:0.324868:0.000000
obtenemos:@0.645003:0.341229:0.733069:0.341229:0.733069:0.324605:0.645003:0.324605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 los valores de la va-:@0.733069:0.341229:0.879901:0.341229:0.879901:0.324840:0.733069:0.324840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
riable , por último, :@0.115209:0.357825:0.258539:0.357825:0.258539:0.341436:0.115209:0.341436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y:@0.156008:0.357825:0.166806:0.357825:0.166806:0.341464:0.156008:0.341464:0.000000:0.000000
organizamos :@0.258539:0.357825:0.361714:0.357825:0.361714:0.341201:0.258539:0.341201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los datos en forma de tabla.:@0.361714:0.357825:0.563992:0.357825:0.563992:0.341436:0.361714:0.341436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ecuación lineal con dos incógnitas:@0.115891:0.141978:0.623187:0.141978:0.623187:0.101242:0.115891:0.101242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M4.1.53. Reconocer la recta como la solución grafica de una ecuación lineal con dos incógnitas en  .:@0.125388:0.074999:0.594677:0.074999:0.594677:0.064570:0.125388:0.064570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.584293:0.074454:0.592760:0.074454:0.592760:0.066269:0.584293:0.066269:0.000000
14:@0.048229:0.122645:0.082283:0.122645:0.082283:0.065614:0.048229:0.065614:0.000000:0.000000
x:@0.159366:0.389972:0.167642:0.389972:0.167642:0.374608:0.159366:0.374608:0.000000
–3:@0.250684:0.389972:0.267235:0.389972:0.267235:0.375073:0.250684:0.375073:0.000000:0.000000
–2:@0.346139:0.389972:0.362690:0.389972:0.362690:0.375073:0.346139:0.375073:0.000000:0.000000
–1:@0.441594:0.389972:0.458145:0.389972:0.458145:0.375073:0.441594:0.375073:0.000000:0.000000
0:@0.541237:0.389972:0.549412:0.389972:0.549412:0.375073:0.541237:0.375073:0.000000
1:@0.636692:0.389972:0.644868:0.389972:0.644868:0.375073:0.636692:0.375073:0.000000
2:@0.732148:0.389972:0.740323:0.389972:0.740323:0.375073:0.732148:0.375073:0.000000
3:@0.827603:0.389972:0.835778:0.389972:0.835778:0.375073:0.827603:0.375073:0.000000
y:@0.159266:0.414917:0.167642:0.414917:0.167642:0.399553:0.159266:0.399553:0.000000
18:@0.250734:0.414917:0.267084:0.414917:0.267084:0.400018:0.250734:0.400018:0.000000:0.000000
17:@0.346189:0.414917:0.362539:0.414917:0.362539:0.400018:0.346189:0.400018:0.000000:0.000000
16:@0.441644:0.414917:0.457995:0.414917:0.457995:0.400018:0.441644:0.400018:0.000000:0.000000
15:@0.537099:0.414917:0.553450:0.414917:0.553450:0.400018:0.537099:0.400018:0.000000:0.000000
14:@0.632555:0.414917:0.648905:0.414917:0.648905:0.400018:0.632555:0.400018:0.000000:0.000000
13:@0.728010:0.414917:0.744360:0.414917:0.744360:0.400018:0.728010:0.400018:0.000000:0.000000
12:@0.823465:0.414917:0.839815:0.414917:0.839815:0.400018:0.823465:0.400018:0.000000:0.000000
–5 0:@0.189896:0.509395:0.219099:0.509395:0.219099:0.497476:0.189896:0.497476:0.000000:0.000000:0.000000:0.000000
10:@0.273015:0.509395:0.286095:0.509395:0.286095:0.497476:0.273015:0.497476:0.000000:0.000000
15:@0.301976:0.509395:0.315056:0.509395:0.315056:0.497476:0.301976:0.497476:0.000000:0.000000
20:@0.328901:0.509395:0.341981:0.509395:0.341981:0.497476:0.328901:0.497476:0.000000:0.000000
5:@0.248570:0.509395:0.255110:0.509395:0.255110:0.497476:0.248570:0.497476:0.000000
20:@0.203767:0.464173:0.216847:0.464173:0.216847:0.452254:0.203767:0.452254:0.000000:0.000000
y:@0.231447:0.444174:0.236208:0.444174:0.236208:0.433763:0.231447:0.433763:0.000000
x:@0.357532:0.495678:0.362281:0.495678:0.362281:0.485267:0.357532:0.485267:0.000000
–4:@0.229956:0.773964:0.243197:0.773964:0.243197:0.762045:0.229956:0.762045:0.000000:0.000000
–2:@0.284529:0.773964:0.297770:0.773964:0.297770:0.762045:0.284529:0.762045:0.000000:0.000000
–2:@0.328339:0.809289:0.341581:0.809289:0.341581:0.797370:0.328339:0.797370:0.000000:0.000000
–4:@0.328339:0.851917:0.341581:0.851917:0.341581:0.839998:0.328339:0.839998:0.000000:0.000000
–6:@0.328339:0.895450:0.341581:0.895450:0.341581:0.883531:0.328339:0.883531:0.000000:0.000000
0:@0.335456:0.773964:0.341996:0.773964:0.341996:0.762045:0.335456:0.762045:0.000000
2:@0.398418:0.773964:0.404958:0.773964:0.404958:0.762045:0.398418:0.762045:0.000000
y:@0.355902:0.747288:0.360663:0.747288:0.360663:0.736876:0.355902:0.736876:0.000000
x:@0.450349:0.758448:0.455098:0.758448:0.455098:0.748036:0.450349:0.748036:0.000000
Sí.:@0.577732:0.648738:0.592825:0.648738:0.592825:0.632349:0.577732:0.632349:0.000000:0.000000:0.000000
Pendiente   = 1:@0.575539:0.915290:0.693440:0.915290:0.693440:0.898901:0.575539:0.898901:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.651793:0.915290:0.666425:0.915290:0.666425:0.898929:0.651793:0.898929:0.000000
Posible respuesta A( 3, 0) B(10, 7):@0.575539:0.717793:0.805166:0.717793:0.805166:0.701404:0.575539:0.701404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(8, 2)  no es solución:@0.597782:0.785880:0.741112:0.785880:0.741112:0.769491:0.597782:0.769491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(9, –2)  no es solución:@0.597782:0.834825:0.750068:0.834825:0.750068:0.818436:0.597782:0.818436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(20, 17) sí es solución:@0.597782:0.861227:0.745848:0.861227:0.745848:0.844838:0.597782:0.844838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(–4, –7)   sí es solución:@0.597782:0.809682:0.753845:0.809682:0.753845:0.793293:0.597782:0.793293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–6:@0.224640:0.692912:0.242589:0.692912:0.242589:0.676523:0.224640:0.676523:0.000000:0.000000
–2:@0.281029:0.668848:0.298978:0.668848:0.298978:0.652459:0.281029:0.652459:0.000000:0.000000
–4:@0.337528:0.692912:0.355477:0.692912:0.355477:0.676523:0.337528:0.676523:0.000000:0.000000
–3:@0.393474:0.692912:0.411423:0.692912:0.411423:0.676523:0.393474:0.676523:0.000000:0.000000
–2:@0.450526:0.692912:0.468475:0.692912:0.468475:0.676523:0.450526:0.676523:0.000000:0.000000
E:@0.376270:0.800837:0.382515:0.800837:0.382515:0.788917:0.376270:0.788917:0.000000
D:@0.349466:0.824715:0.358137:0.824715:0.358137:0.812796:0.349466:0.812796:0.000000
C:@0.326441:0.843605:0.334080:0.843605:0.334080:0.831686:0.326441:0.831686:0.000000
B:@0.292253:0.867303:0.299021:0.867303:0.299021:0.855383:0.292253:0.855383:0.000000
A:@0.268277:0.889934:0.276117:0.889934:0.276117:0.878015:0.268277:0.878015:0.000000