Solve for x, y, z
x=1
y=2
z=3
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z=-3x+2y+2
Solve 3x-2y+z=2 for z.
2x+3y-\left(-3x+2y+2\right)=5 x+y-3x+2y+2=6
Substitute -3x+2y+2 for z in the second and third equation.
y=-5x+7 x=\frac{3}{2}y-2
Solve these equations for y and x respectively.
x=\frac{3}{2}\left(-5x+7\right)-2
Substitute -5x+7 for y in the equation x=\frac{3}{2}y-2.
x=1
Solve x=\frac{3}{2}\left(-5x+7\right)-2 for x.
y=-5+7
Substitute 1 for x in the equation y=-5x+7.
y=2
Calculate y from y=-5+7.
z=-3+2\times 2+2
Substitute 2 for y and 1 for x in the equation z=-3x+2y+2.
z=3
Calculate z from z=-3+2\times 2+2.
x=1 y=2 z=3
The system is now solved.
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