Answer
$x=-6$
$y=4$
$z=-4$
Work Step by Step
The third equation: $x-y-2z=-2$
Solve for x: $\rightarrow x=y+2z-2$
Substitute for z in the first equation:
$4x + y +5z = -40$
$4(y+2z-2)+ y+ 5z = -40$
$4y+8z-8+ y+ 5z= -40$
$5y+13z=-32$ (1)
Substitute for z in the second equation:
$-3x + 2y + 4z = 10$
$-3(y+2z-2)+ 2y + 4z = 10$
$-y-2z=4$
$\rightarrow y=-2z-4$
Substitute for y in equation (1):
$5(-2z-4)+13z=-32$
$3z=-12$
$z=-4$
Solve for y: $y=-2z-4$
$y=-2(-4)-4$
$y=4$
Solve for x: $x=y+2z-2$
$x=4+2(-4)-2$
$x=-6$
