136:@0.024814:0.963884:0.056738:0.963884:0.056738:0.945447:0.024814:0.945447:0.000000:0.000000:0.000000
M.4.1.53.:@0.096359:0.941084:0.142269:0.941084:0.142269:0.930329:0.096359:0.930329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Reconocer la recta como la solución gráfica de una ecuación lineal con dos incógnitas en R.:@0.142269:0.941084:0.571002:0.941084:0.571002:0.931112:0.142269:0.931112:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ecuaciones lineales con dos incógnitas:@0.305303:0.084620:0.860840:0.084620:0.860840:0.053892:0.305303:0.053892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 1:@0.124729:0.083964:0.219414:0.083964:0.219414:0.055923:0.124729:0.055923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las  ecuaciones  lineales  con  dos  incógnitas  también  son conocidas como :@0.304744:0.203386:0.907134:0.203386:0.907134:0.187716:0.304744:0.187716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuaciones indeterminadas, ya que tienen una infinidad de soluciones que son :@0.304744:0.219982:0.907104:0.219982:0.907104:0.204313:0.304744:0.204313:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pares de números que verifican la ecuación. Veamos un ejemplo de aplicación de :@0.304744:0.236579:0.907088:0.236579:0.907088:0.220909:0.304744:0.220909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuaciones lineales.:@0.304744:0.253175:0.449307:0.253175:0.449307:0.237505:0.304744:0.237505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para la nota de su parcial, Fabián rindió dos exámenes de matemática. Si su :@0.304744:0.276894:0.907051:0.276894:0.907051:0.261224:0.304744:0.261224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
profesora le dice que la suma de sus calificaciones es 14, ¿qué calificación obtuvo :@0.304744:0.293491:0.907162:0.293491:0.907162:0.277821:0.304744:0.277821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Fabián en cada examen?:@0.304744:0.310087:0.485021:0.310087:0.485021:0.294417:0.304744:0.294417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los datos que desconocemos son las variables, siendo   el primer examen y   el :@0.304744:0.333806:0.907069:0.333806:0.907069:0.318136:0.304744:0.318136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.715053:0.333806:0.722517:0.333806:0.722517:0.317445:0.715053:0.317445:0.000000
y:@0.877530:0.333806:0.885012:0.333806:0.885012:0.317445:0.877530:0.317445:0.000000
segundo examen.:@0.304744:0.350402:0.436428:0.350402:0.436428:0.334732:0.304744:0.334732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La ecuación planteada es:   +   = 14:@0.304744:0.374121:0.568220:0.374121:0.568220:0.358451:0.304744:0.358451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.497182:0.374121:0.504645:0.374121:0.504645:0.357760:0.497182:0.357760:0.000000
y:@0.523699:0.374121:0.531181:0.374121:0.531181:0.357760:0.523699:0.357760:0.000000
Definición de ecuación lineal:@0.319266:0.402789:0.555037:0.402789:0.555037:0.385888:0.319266:0.385888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Es una expresión de la forma :@0.555037:0.402789:0.791777:0.402789:0.791777:0.387119:0.555037:0.387119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax:@0.794375:0.402789:0.811107:0.402789:0.811107:0.386428:0.794375:0.386428:0.000000:0.000000
 + :@0.811107:0.402789:0.832760:0.402789:0.832760:0.387119:0.811107:0.387119:0.000000:0.000000:0.000000
by:@0.835358:0.402789:0.851998:0.402789:0.851998:0.386428:0.835358:0.386428:0.000000:0.000000
 =  ,  :@0.852046:0.402789:0.891223:0.402789:0.891223:0.387119:0.852046:0.387119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.876297:0.402789:0.883963:0.402789:0.883963:0.386428:0.876297:0.386428:0.000000
donde  ,   y   son números reales y el grado de las incógnitas     es 1.:@0.315931:0.419385:0.837557:0.419385:0.837557:0.403716:0.315931:0.403716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.368634:0.419385:0.418260:0.419385:0.418260:0.403024:0.368634:0.403024:0.000000:0.000000:0.000000:0.000000:0.000000
x e y:@0.771880:0.419565:0.801475:0.419565:0.801475:0.403812:0.771880:0.403812:0.000000:0.000000:0.000000:0.000000:0.000000
A continuación, resolveremos la ecuación planteada anteriormente.:@0.304744:0.451763:0.799924:0.451763:0.799924:0.436094:0.304744:0.436094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Primero  :@0.304744:0.475482:0.377330:0.475482:0.377330:0.458347:0.304744:0.458347:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: despejamos la variable  .:@0.370401:0.475482:0.558912:0.475482:0.558912:0.459813:0.370401:0.459813:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.548224:0.475482:0.555706:0.475482:0.555706:0.459121:0.548224:0.459121:0.000000
y:@0.304744:0.499201:0.312225:0.499201:0.312225:0.482840:0.304744:0.482840:0.000000
 = 14 – :@0.312225:0.499201:0.366550:0.499201:0.366550:0.483532:0.312225:0.483532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.366550:0.499201:0.374013:0.499201:0.374013:0.482840:0.366550:0.482840:0.000000
Segundo:@0.304744:0.522920:0.378491:0.522920:0.378491:0.505785:0.304744:0.505785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: asignamos valores positivos arbitrarios a  , efectuamos las operaciones :@0.378491:0.522920:0.907138:0.522920:0.907138:0.507251:0.378491:0.507251:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.682949:0.522920:0.692126:0.522920:0.692126:0.505812:0.682949:0.505812:0.000000
y obtenemos los valores de  . Organizamos los datos en una tabla de valores.:@0.304744:0.539517:0.867387:0.539517:0.867387:0.523847:0.304744:0.523847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.509102:0.539517:0.516584:0.539517:0.516584:0.523155:0.509102:0.523155:0.000000
Como se puede observar, estas son algunas soluciones para el problema planteado.:@0.304744:0.563236:0.902829:0.563236:0.902829:0.547566:0.304744:0.547566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.304744:0.673449:0.308779:0.673449:0.308779:0.657780:0.304744:0.657780:0.000000
x:@0.364469:0.592185:0.372812:0.592185:0.372812:0.576632:0.364469:0.576632:0.000000
y:@0.453776:0.592185:0.462102:0.592185:0.462102:0.576632:0.453776:0.576632:0.000000
 = 14 – :@0.462102:0.592185:0.512594:0.592185:0.512594:0.576607:0.462102:0.576607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.512594:0.592185:0.520937:0.592185:0.520937:0.576632:0.512594:0.576632:0.000000
y:@0.601918:0.592185:0.610244:0.592185:0.610244:0.576632:0.601918:0.576632:0.000000
Si   = 4:@0.345037:0.618287:0.392262:0.618287:0.392262:0.604041:0.345037:0.604041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.359980:0.618287:0.366764:0.618287:0.366764:0.603413:0.359980:0.603413:0.000000
y:@0.455184:0.618287:0.461985:0.618287:0.461985:0.603413:0.455184:0.603413:0.000000
 = 14 – 4:@0.461985:0.618287:0.519546:0.618287:0.519546:0.604041:0.461985:0.604041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.585852:0.618287:0.592654:0.618287:0.592654:0.603413:0.585852:0.603413:0.000000
 = 10:@0.592654:0.618287:0.626326:0.618287:0.626326:0.604041:0.592654:0.604041:0.000000:0.000000:0.000000:0.000000:0.000000
Si   = 5:@0.345037:0.641974:0.392262:0.641974:0.392262:0.627729:0.345037:0.627729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.359980:0.641974:0.366764:0.641974:0.366764:0.627100:0.359980:0.627100:0.000000
y :@0.455519:0.641974:0.465336:0.641974:0.465336:0.627100:0.455519:0.627100:0.000000:0.000000
= 14 – 5:@0.465336:0.641974:0.519228:0.641974:0.519228:0.627729:0.465336:0.627729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.589940:0.641974:0.596741:0.641974:0.596741:0.627100:0.589940:0.627100:0.000000
 = 9:@0.596741:0.641974:0.622238:0.641974:0.622238:0.627729:0.596741:0.627729:0.000000:0.000000:0.000000:0.000000
Si   = 7:@0.345037:0.665662:0.392262:0.665662:0.392262:0.651416:0.345037:0.651416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.359980:0.665662:0.366764:0.665662:0.366764:0.650788:0.359980:0.650788:0.000000
y :@0.455519:0.665662:0.465336:0.665662:0.465336:0.650788:0.455519:0.650788:0.000000:0.000000
= 14 – 7:@0.465336:0.665662:0.519228:0.665662:0.519228:0.651416:0.465336:0.651416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.589940:0.665662:0.596741:0.665662:0.596741:0.650788:0.589940:0.650788:0.000000
 = 7:@0.596741:0.665662:0.622238:0.665662:0.622238:0.651416:0.596741:0.651416:0.000000:0.000000:0.000000:0.000000
 :@0.665937:0.673476:0.669973:0.673476:0.669973:0.657806:0.665937:0.657806:0.000000
a) :@0.304737:0.697195:0.323975:0.697195:0.323975:0.680059:0.304737:0.680059:0.000000:0.000000:0.000000
Si en el primer examen obtuvo 4, en el segundo sacó 10.:@0.333226:0.697195:0.746941:0.697195:0.746941:0.681525:0.333226:0.681525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b) :@0.304737:0.720914:0.325118:0.720914:0.325118:0.703778:0.304737:0.703778:0.000000:0.000000:0.000000
Si en el primer examen obtuvo 5, en el segundo sacó 9.:@0.333226:0.720914:0.737949:0.720914:0.737949:0.705244:0.333226:0.705244:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c) :@0.304737:0.744633:0.322557:0.744633:0.322557:0.727497:0.304737:0.727497:0.000000:0.000000:0.000000
Si en el primer examen obtuvo 7, en el segundo sacó 7.:@0.333226:0.744633:0.737949:0.744633:0.737949:0.728963:0.333226:0.728963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Podemos concluir que para todo valor de  , existe uno para  . Por lo tanto, no hay :@0.304737:0.768352:0.907151:0.768352:0.907151:0.752682:0.304737:0.752682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.613877:0.768352:0.621340:0.768352:0.621340:0.751990:0.613877:0.751990:0.000000
y:@0.745393:0.768352:0.752875:0.768352:0.752875:0.751990:0.745393:0.751990:0.000000
 :@0.903082:0.768352:0.907118:0.768352:0.907118:0.752682:0.903082:0.752682:0.000000
solución única para el problema.:@0.304737:0.784948:0.543170:0.784948:0.543170:0.769278:0.304737:0.769278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recuerda. :@0.311168:0.166125:0.394109:0.166125:0.394109:0.149224:0.311168:0.149224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo puedes graficar la ecuación de una recta? :@0.394109:0.166125:0.757847:0.166125:0.757847:0.150455:0.394109:0.150455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.344861:0.139515:0.470369:0.139515:0.470369:0.122615:0.344861:0.122615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.160410:0.909708:0.165028:0.909708:0.165028:0.901292:0.160410:0.901292:0.000000
0:@0.141959:0.907577:0.146577:0.907577:0.146577:0.899162:0.141959:0.899162:0.000000
0:@0.134257:0.900653:0.138875:0.900653:0.138875:0.892238:0.134257:0.892238:0.000000
4:@0.182532:0.909708:0.187149:0.909708:0.187149:0.901292:0.182532:0.901292:0.000000
6:@0.204654:0.909708:0.209271:0.909708:0.209271:0.901292:0.204654:0.901292:0.000000
8:@0.226852:0.909708:0.231469:0.909708:0.231469:0.901292:0.226852:0.901292:0.000000
10:@0.246883:0.909708:0.256117:0.909708:0.256117:0.901292:0.246883:0.901292:0.000000:0.000000
12:@0.268957:0.909708:0.278192:0.909708:0.278192:0.901292:0.268957:0.901292:0.000000:0.000000
14:@0.291117:0.909708:0.300352:0.909708:0.300352:0.901292:0.291117:0.901292:0.000000:0.000000
16:@0.313192:0.909708:0.322427:0.909708:0.322427:0.901292:0.313192:0.901292:0.000000:0.000000
-2:@0.114753:0.909708:0.122190:0.909708:0.122190:0.901292:0.114753:0.901292:0.000000:0.000000
2:@0.132030:0.890759:0.136647:0.890759:0.136647:0.882344:0.132030:0.882344:0.000000
4:@0.132030:0.877025:0.136647:0.877025:0.136647:0.868610:0.132030:0.868610:0.000000
6:@0.132030:0.863866:0.136647:0.863866:0.136647:0.855451:0.132030:0.855451:0.000000
8:@0.132030:0.850352:0.136647:0.850352:0.136647:0.841937:0.132030:0.841937:0.000000
10:@0.127687:0.836803:0.136922:0.836803:0.136922:0.828388:0.127687:0.828388:0.000000:0.000000
12:@0.127689:0.823530:0.136924:0.823530:0.136924:0.815115:0.127689:0.815115:0.000000:0.000000
14:@0.127642:0.809980:0.136877:0.809980:0.136877:0.801565:0.127642:0.801565:0.000000:0.000000
y:@0.131869:0.799410:0.136032:0.799410:0.136032:0.790994:0.131869:0.790994:0.000000
x:@0.334064:0.909786:0.338123:0.909786:0.338123:0.901370:0.334064:0.901370:0.000000
A:@0.187676:0.834346:0.195783:0.834346:0.195783:0.822396:0.187676:0.822396:0.000000
B:@0.198843:0.841136:0.206023:0.841136:0.206023:0.829186:0.198843:0.829186:0.000000
C:@0.220899:0.855015:0.228582:0.855015:0.228582:0.843065:0.220899:0.843065:0.000000
Shutterstock, 124139695 :@0.090147:0.342738:0.090147:0.267119:0.078759:0.267119:0.078759:0.342738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Con el objetivo de :@0.104573:0.558507:0.230415:0.558507:0.230415:0.544262:0.104573:0.544262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
construir una tabla :@0.104573:0.573595:0.233315:0.573595:0.233315:0.559349:0.104573:0.559349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de valores, se asignan :@0.104573:0.588682:0.252260:0.588682:0.252260:0.574437:0.104573:0.574437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
valores arbitrarios :@0.104573:0.603770:0.225557:0.603770:0.225557:0.589525:0.104573:0.589525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a la variable   para :@0.104573:0.618857:0.230132:0.618857:0.230132:0.604612:0.104573:0.604612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.186609:0.618857:0.193394:0.618857:0.193394:0.603984:0.186609:0.603984:0.000000
reemplazar en la :@0.104573:0.633945:0.218272:0.633945:0.218272:0.619700:0.104573:0.619700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuación y obtener el :@0.104573:0.649033:0.252663:0.649033:0.252663:0.634787:0.104573:0.634787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
valor de  .:@0.104573:0.664120:0.171449:0.664120:0.171449:0.649875:0.104573:0.649875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.161732:0.664120:0.168534:0.664120:0.168534:0.649246:0.161732:0.649246:0.000000
Responde: :@0.104573:0.686337:0.181567:0.686337:0.181567:0.671224:0.104573:0.671224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿qué es una :@0.181567:0.686337:0.264910:0.686337:0.264910:0.672092:0.181567:0.672092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tabla de valores?:@0.104573:0.701424:0.215489:0.701424:0.215489:0.687179:0.104573:0.687179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.139934:0.522150:0.260561:0.522150:0.260561:0.505249:0.139934:0.505249:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.139934:0.534721:0.234375:0.534721:0.234375:0.517821:0.139934:0.517821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Como se pude observar, la :@0.708942:0.826336:0.907131:0.826336:0.907131:0.810666:0.708942:0.810666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
solución es una línea recta, :@0.708942:0.842932:0.907131:0.842932:0.907131:0.827263:0.708942:0.827263:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
donde cada par ordenado :@0.708942:0.859529:0.907095:0.859529:0.907095:0.843859:0.708942:0.843859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ) de la recta satisface la :@0.708942:0.876125:0.907161:0.876125:0.907161:0.860455:0.708942:0.860455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.713826:0.876125:0.735994:0.876125:0.735994:0.859764:0.713826:0.859764:0.000000:0.000000:0.000000
ecuación.:@0.708942:0.892721:0.779207:0.892721:0.779207:0.877052:0.708942:0.877052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.462362:0.812929:0.470705:0.812929:0.470705:0.797377:0.462362:0.797377:0.000000
y:@0.547849:0.812929:0.556175:0.812929:0.556175:0.797377:0.547849:0.797377:0.000000
Puntos:@0.611458:0.812929:0.663508:0.812929:0.663508:0.797351:0.611458:0.797351:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.430918:0.839295:0.439093:0.839295:0.439093:0.825050:0.430918:0.825050:0.000000
10:@0.516388:0.839295:0.532739:0.839295:0.532739:0.825050:0.516388:0.825050:0.000000:0.000000
A (4, 10):@0.601859:0.839295:0.655316:0.839295:0.655316:0.825050:0.601859:0.825050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.430901:0.864780:0.439076:0.864780:0.439076:0.850535:0.430901:0.850535:0.000000
9:@0.516372:0.864780:0.524547:0.864780:0.524547:0.850535:0.516372:0.850535:0.000000
B (5, 9):@0.601842:0.864780:0.645784:0.864780:0.645784:0.850535:0.601842:0.850535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
7:@0.430884:0.890266:0.439059:0.890266:0.439059:0.876021:0.430884:0.876021:0.000000
7:@0.516355:0.890266:0.524530:0.890266:0.524530:0.876021:0.516355:0.876021:0.000000
C (7, 7):@0.601826:0.890266:0.646856:0.890266:0.646856:0.876021:0.601826:0.876021:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para graficar una recta basta dos puntos de la misma.:@0.311168:0.172492:0.558376:0.172492:0.558376:0.162520:0.311168:0.162520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000