Answer
The solution is $(-1,4,2)$.
Work Step by Step
Rewrite the system as a linear system in two variables.
Add Equation 1 and Equation 3. Then add Equation 2 to 5 times Equation 3:
$ x -y + z = -3$
$4x +2y - z = 2$
_____________________
$5x+y=-1$
$2x - y + 5z = 4$
$20x + 10y - 5z = 10$
__________________________
$22x+9y=14$
Solve the new linear system for both of its variables.
$5x+y=-1$
$22x+9y=14$
Add $-9$ times new Equation 1 to new Equation 2:
$-45x-9y=9$
$22x+9y=14$
___________________
$-23x=23$
$x=-1$
Solve for y: $5(-1)+y=-1$
$y=4$
Solve for z: $-1-4+z=-3$
$z=2$
The solution is $(-1,4,2)$.
