Answer
$(7,-4,-2)$ is the solution of the system.
Work Step by Step
Given: $x+2y=-1$
$\rightarrow x=-2y-1$
Substitute for x in the second equation:
$3x- y + 4z = 17$
$3(-2y-1)- y + 4z = 17$
$-6y-3-y+4z=17$
$-7y+4z=20$ (1)
Then continue to substitute for x in the third equation:
$-4x + 2y - 3z = -30$
$-4(-2y-1) + 2y - 3z = -30$
$8y+4+2y-3z=-30$
$10y-3z=-34$ (2)
From (1) and (2) we get the system of equations:
$-7y+4z=20$
$10y-3z=-34$
Multiply both sides of the first equation by $10$ and the second equation by $7$:
$-70y+40z=200$
$70y-21z=-238$
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$19z=-38$
$z=-2$
Solve for y: $-7y+4z=20$
$-7y+4(-2)=20$
$-7y=28$
$y=-4$
Solve for x: $x=-2y-1$
$x=-2(-4)-1=7$
$(7,-4,-2)$ is the solution of the system.
