Answer
The solution is $(5, 9,-6)$
Work Step by Step
Rewrite the system as a linear system in two variables.
Add Equation 1 and $5$ times Equation 3. Then add Equation 2 to Equation 3:
$5x + y - z =40$
$-5x + 15y + 5z = 80$
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$16y+4z=120$
$x + 7y +4z = 44$
$-x + 3y + z = 16$
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$10y+5z=60$
Solve the new linear system for both of its variables.
$16y+4z=120$
$10y+5z=60$
Add $5$ times new Equation 1 to $-4$ times new Equation 2:
$80y+20z=600$
$-40y-20z=-240$
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$40y=360$
$y=9$
Solve for z: $10(9)+5z=60$
$5z=-30$
$z=-6$
Solve for y: $x+7(9)+4(-6)=44$
$x=5$
The solution is $(5, 9,-6)$.
