Solve for x, y, z
x=2
y=2
z=2
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x=5y-3z-2
Solve x-5y+3z=-2 for x.
4\left(5y-3z-2\right)-13y+20z=22 2\left(5y-3z-2\right)-y+3z=8
Substitute 5y-3z-2 for x in the second and third equation.
y=\frac{30}{7}-\frac{8}{7}z z=-4+3y
Solve these equations for y and z respectively.
z=-4+3\left(\frac{30}{7}-\frac{8}{7}z\right)
Substitute \frac{30}{7}-\frac{8}{7}z for y in the equation z=-4+3y.
z=2
Solve z=-4+3\left(\frac{30}{7}-\frac{8}{7}z\right) for z.
y=\frac{30}{7}-\frac{8}{7}\times 2
Substitute 2 for z in the equation y=\frac{30}{7}-\frac{8}{7}z.
y=2
Calculate y from y=\frac{30}{7}-\frac{8}{7}\times 2.
x=5\times 2-3\times 2-2
Substitute 2 for y and 2 for z in the equation x=5y-3z-2.
x=2
Calculate x from x=5\times 2-3\times 2-2.
x=2 y=2 z=2
The system is now solved.
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