Answer
$(2,6,-5)$ is a solution of the system.
Work Step by Step
Use elimination for the first and second equations:
$x + y + z = 3$
$-x + 5y + z = 23$
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$6y+2z=26$ (1)
Then continue to use elimination for the second and third equations:
$3x - 4y + 2z=-28$
$-x + 5y + z = 23$
Multiply both sides of the first equation by $3$:
$3x - 4y + 2z=-28$
$-3x + 15y + 3z = 69$
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$11y+5z=41$ (2)
From (1) and (2):
$6y+2z=26$
$11y+5z=41$
Multiply both sides of the first equation by $-5$ and the second equation by $2$:
$-30y-10z=-130$
$22y+10z=82$
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$-8y=-48$
$y=6$
Solve for z: $11(6)+5z=41$
$5z=-25$
$z=-5$
Solve for x: $x+6+(-5)=3$
$x=2$
$(2,6,-5)$ is a solution of the system.
