Answer
The solution is $(-3, -8,4)$.
Work Step by Step
Rewrite the system as a linear system in two variables.
Add Equation 1 and $6$ times Equation 2. Then add $2$ times Equation 2 to Equation 3:
$6x - y + 4z =6$
$-6x -18y +6z = 186$
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$-19y+10z=192$
$-2x -6y + 2z = 62$
$2x + 2y- 5z =-42$
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$-4y-3z=20$
Solve the new linear system for both of its variables.
$-19y+10z=192$
$-4y-3z=20$
Now, we can eliminate z:
$-57y+30z=576$
$-40y-30z=200$
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$-97y=776$
$y=-8$
Solve for z: $-4(-8)-3z=20$
$12=3z$
$z=4$
Solve for y: $-x-3(-8)+4=31$
$x=-3$
The solution is $(-3, -8,4)$
