Solve for x, y, z
x=2
y=-1
z=-1
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x=y-2z+1
Solve x-y+2z=1 for x.
y-2z+1+3y-z=0 2\left(y-2z+1\right)+3y-z=2
Substitute y-2z+1 for x in the second and third equation.
y=\frac{3}{4}z-\frac{1}{4} z=y
Solve these equations for y and z respectively.
z=\frac{3}{4}z-\frac{1}{4}
Substitute \frac{3}{4}z-\frac{1}{4} for y in the equation z=y.
z=-1
Solve z=\frac{3}{4}z-\frac{1}{4} for z.
y=\frac{3}{4}\left(-1\right)-\frac{1}{4}
Substitute -1 for z in the equation y=\frac{3}{4}z-\frac{1}{4}.
y=-1
Calculate y from y=\frac{3}{4}\left(-1\right)-\frac{1}{4}.
x=-1-2\left(-1\right)+1
Substitute -1 for y and -1 for z in the equation x=y-2z+1.
x=2
Calculate x from x=-1-2\left(-1\right)+1.
x=2 y=-1 z=-1
The system is now solved.
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