Solve for x, y, z
x=1
y=0
z=1
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x=-y+z
Solve x+y-z=0 for x.
3\left(-y+z\right)+2y+z=4 -y+z-3y+4z=5
Substitute -y+z for x in the second and third equation.
y=-4+4z z=\frac{4}{5}y+1
Solve these equations for y and z respectively.
z=\frac{4}{5}\left(-4+4z\right)+1
Substitute -4+4z for y in the equation z=\frac{4}{5}y+1.
z=1
Solve z=\frac{4}{5}\left(-4+4z\right)+1 for z.
y=-4+4\times 1
Substitute 1 for z in the equation y=-4+4z.
y=0
Calculate y from y=-4+4\times 1.
x=-0+1
Substitute 0 for y and 1 for z in the equation x=-y+z.
x=1
Calculate x from x=-0+1.
x=1 y=0 z=1
The system is now solved.
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