Answer
$(-1,4,0)$ is the solution of the system.
Work Step by Step
Using elimination for the second and the third equations:
$x +6y +3z =23$
$-x + y + 2z = 5$
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$7y+5z=28$ (1)
Then continue to use elimination for the first and the third equations:
$6x + y - z =-2 $
$-x + y + 2z = 5$
Multiply both sides of the second equation by $6$:
$6x + y - z =-2 $
$-6x + 6y + 12z = 30$
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$7y+11z=28$(2)
Using elimination for equation (1) and (2):
$7y+5z=28$
$7y+11z=28$
Multiply both sides of the first equation by $-1$:
$-7y-5z=-28$
$7y+11z=28$
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$6z=0$
$z=0$
Solve for y: $7y+5(0)=28$
$7y=28$
$y=4$
Solve for x: $x+6(4)+3(0)=23$
$x+24=23$
$x=-1$
$(-1,4,0)$ is the solution of the system.
