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