Question

resolve o sistema de equacao linear
2x+3y-2z=9
x-3y+z=-2
3x+2y-z=9

Answer 1

Resposta:

(x,y,z) = (2,1,-1)

Explicação passo-a-passo:

Considere dois pares de equações: $\left \{ {{2x+3y-2z=9} \atop {x-3y+z=-2}} \right. \\\left \{ {{x-3y+z=-2} \atop {3x+2y-z=9}} \right.$

$\left \{ {{2x+3y-2z=9} \atop {x-3y+z=-2}} \right. = 3x-z= 7$

$\left \{ {{x-3y+z=-2} \atop {3x+2y-z=9}} \right. = 11x-z= 23$

$\left \{ {{3x-z=7} \atop {11x-z=23}} \right. \\z = -1x = 2$

Substitua os valores de z,x na equação 3x+2y-z=9 -> 3.2+2y-(-1)=9

Valor de y -> 3.2+2y-(-1)=9  y=1

(x,y,z) = (2,1,-1)

$\left \{ {{2.2+3.1-2.(-1)=9} \atop {2-3.1+(-1)=-2}} \right. \\\left \{ {{3.2+2.1-(-1)=9} \atop {}} \right. \\9=9\\-2=-2\\9=9\\\left \{ {{9=9} \atop {-2=-2\\}} \right.\\9=9\\(x,y,z) = (2,1,-1)$