Answer
$(8,1,1)$ is a solution of the system.
Work Step by Step
Use elimination for the first two equations:
$2x - y + 4z = 19$
$-x + 3y - 2z = -7 $
Multiply both sides of the second equation by $2$:
$2x - y + 4z = 19$
$-2x + 6y - 4z = -14 $
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$5y=5$
$y=1$
Then continue to use elimination for the first and third equations.
$2x - y + 4z = 19$
$4x + 2y + 3z = 37$
Multiply both sides of the first equation by $-2$.
$-4x +2 y -8z =-38$
$4x + 2y + 3z = 37$
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$4y-5z=-1$
$4(1)-5z=-1$
$5z=5$
$z=1$
Solve for x: $-x+3(1)-2(1)=-7$
$x=8$
$(8,1,1)$ is a solution of the system.
