Answer
The solution is $(5,1,-3)$.
Work Step by Step
Use elimination for equation 1 and equation 2:
$x + y + z = 3 $
$-x + 3y + 2z= -8$
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$4y+3z=-5$
The third equation: $5y+z=2$
$\rightarrow z=2-5y$
Substitute for z:
$4y+3z=-5$
$4y+3(2-5y)=-5$
$-11y=-11$
$y=1$
Solve for z: $z=2-5(1)=-3$
Solve for x: $x+1+(-3)=3$
$x=5$
The solution is $(5,1,-3)$.
