Solve for x, y, z
x=-3
y=-6
z=-1
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z=-3x+2y+2
Solve 3x-2y+z=2 for z.
x-y+2\left(-3x+2y+2\right)=1 2x+y-3\left(-3x+2y+2\right)=-9
Substitute -3x+2y+2 for z in the second and third equation.
y=\frac{5}{3}x-1 x=\frac{5}{11}y-\frac{3}{11}
Solve these equations for y and x respectively.
x=\frac{5}{11}\left(\frac{5}{3}x-1\right)-\frac{3}{11}
Substitute \frac{5}{3}x-1 for y in the equation x=\frac{5}{11}y-\frac{3}{11}.
x=-3
Solve x=\frac{5}{11}\left(\frac{5}{3}x-1\right)-\frac{3}{11} for x.
y=\frac{5}{3}\left(-3\right)-1
Substitute -3 for x in the equation y=\frac{5}{3}x-1.
y=-6
Calculate y from y=\frac{5}{3}\left(-3\right)-1.
z=-3\left(-3\right)+2\left(-6\right)+2
Substitute -6 for y and -3 for x in the equation z=-3x+2y+2.
z=-1
Calculate z from z=-3\left(-3\right)+2\left(-6\right)+2.
x=-3 y=-6 z=-1
The system is now solved.
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