Respuestas
Respuesta:
x = -13/48 , y = 1139/24 y z = 629/48
x-3y +27 = 3 (1)
5x+6y-z = 33 (2)
4x-y +32 = 8 (3)
Método de Sustitución :
1 ) Despejamos a " y " en (1) :
x+3y+27 = 3
x+3y+27-x = 3-x
3y+27 = 3-x
3y+27-27 = 3-x-27
3y = -24-x
3y/3 = (-24-x)/3
y = (-24-x)/3
2 ) Reemplazamos a " y = (-24-x)/3 '' en la ecuación (3) :
4x-((-24-x)/3) + 32 = 8
3(4x)-(3(-24-x)/3)+32 = 8
12x-(-24-x)+32 = 8
12x+24+x+32 = 8
13x+56 = 8
13x+56-56 = 8-56
13x = -48
13x/13 = -48/13
x = -13/48
3 ) Reemplazamos a " x = -13/48 '' en
la ecuación '' x-3y+27 = 3 '' :
x-3y+27 = 3
(-13/48)-3y+27 = 3
-13/48-3y+27-27 = 3-27
-13/48 -3y = -24
48(-13/48)-48(3y) = 48(-24)
-13-144y = -1152
-13-144y+13 = -1152+13
-144y = -1139
-(-144y) = -(-1139)
144y = 1139
144y/144 = 1139/144
y = 1139/144
4 ) Cambiamos a " x = -13/48 '' y a " y = 1139/144 '' en (2) :
5(-13/48)+6(1139/144)-z = 33
-65/48+1139/24 - z = 33
2213/48 - z = 33 ; 33 = 1584/48
2213/48 - z = 1584/48
-z = (1584-2213)/48
-z = -629/48
-(-z) = -(-629/48)
z = 629/48
Explicación paso a paso: