Solve for x, y, z
x=-1
y=3
z=5
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x=-3y+2z-2
Solve x+3y-2z=-2 for x.
-3y+2z-2-2y+3z=8 -3y+2z-2+6y-z=12
Substitute -3y+2z-2 for x in the second and third equation.
y=-2+z z=-3y+14
Solve these equations for y and z respectively.
z=-3\left(-2+z\right)+14
Substitute -2+z for y in the equation z=-3y+14.
z=5
Solve z=-3\left(-2+z\right)+14 for z.
y=-2+5
Substitute 5 for z in the equation y=-2+z.
y=3
Calculate y from y=-2+5.
x=-3\times 3+2\times 5-2
Substitute 3 for y and 5 for z in the equation x=-3y+2z-2.
x=-1
Calculate x from x=-3\times 3+2\times 5-2.
x=-1 y=3 z=5
The system is now solved.
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