Solve for x, y, z
x=4
y=-4
z=5
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y=3x-2z-6
Solve 3x-y-2z=6 for y.
x-6\left(3x-2z-6\right)-6z=-2
Substitute 3x-2z-6 for y in the equation x-6y-6z=-2.
x=\frac{38}{17}+\frac{6}{17}z z=7-\frac{1}{2}x
Solve the second equation for x and the third equation for z.
z=7-\frac{1}{2}\left(\frac{38}{17}+\frac{6}{17}z\right)
Substitute \frac{38}{17}+\frac{6}{17}z for x in the equation z=7-\frac{1}{2}x.
z=5
Solve z=7-\frac{1}{2}\left(\frac{38}{17}+\frac{6}{17}z\right) for z.
x=\frac{38}{17}+\frac{6}{17}\times 5
Substitute 5 for z in the equation x=\frac{38}{17}+\frac{6}{17}z.
x=4
Calculate x from x=\frac{38}{17}+\frac{6}{17}\times 5.
y=3\times 4-2\times 5-6
Substitute 4 for x and 5 for z in the equation y=3x-2z-6.
y=-4
Calculate y from y=3\times 4-2\times 5-6.
x=4 y=-4 z=5
The system is now solved.
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