Solve for x, y, z
x = \frac{3}{2} = 1\frac{1}{2} = 1.5
y = \frac{3}{2} = 1\frac{1}{2} = 1.5
z=1
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x=-y+z+2
Solve x+y-z=2 for x.
2\left(-y+z+2\right)-2y+z=1 -y+z+2-3y=-3
Substitute -y+z+2 for x in the second and third equation.
y=\frac{3}{4}+\frac{3}{4}z z=4y-5
Solve these equations for y and z respectively.
z=4\left(\frac{3}{4}+\frac{3}{4}z\right)-5
Substitute \frac{3}{4}+\frac{3}{4}z for y in the equation z=4y-5.
z=1
Solve z=4\left(\frac{3}{4}+\frac{3}{4}z\right)-5 for z.
y=\frac{3}{4}+\frac{3}{4}\times 1
Substitute 1 for z in the equation y=\frac{3}{4}+\frac{3}{4}z.
y=\frac{3}{2}
Calculate y from y=\frac{3}{4}+\frac{3}{4}\times 1.
x=-\frac{3}{2}+1+2
Substitute \frac{3}{2} for y and 1 for z in the equation x=-y+z+2.
x=\frac{3}{2}
Calculate x from x=-\frac{3}{2}+1+2.
x=\frac{3}{2} y=\frac{3}{2} z=1
The system is now solved.
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