Answer
$x=2$
$y=3$
$z=-2$
Work Step by Step
Express z from the second equation.
$x-2y+3z=-10$
$3y+z=7\rightarrow z=7-3y$
$x+y-z=7$
Substitute $ z=7-3y$ into the first and the third equation.
$x-2y+3(7-3y)=-10$
$x+y-(7-3y)=7$
Simplify.
$x-11y=-31$
$x+4y=14$
Multiply the second equation by -1.
$x+4y=14 \rightarrow -x-4y=-14$
Add the equations to elimiate x.
$-15y=-45$
$y=3$
Substitute for y and solve for x and z.
$z=7-3y\rightarrow z=-2$
$x+4y=14\rightarrow x=2$
