Solve for x, y, z
x=1
y=2
z=2
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x-2=y-3 2y-6=z-4 2x+y+z-6=0
Multiply each equation by the least common multiple of denominators in it. Simplify.
x=-1+y
Solve x-2=y-3 for x.
2\left(-1+y\right)+y+z-6=0
Substitute -1+y for x in the equation 2x+y+z-6=0.
y=1+\frac{1}{2}z z=8-3y
Solve the second equation for y and the third equation for z.
z=8-3\left(1+\frac{1}{2}z\right)
Substitute 1+\frac{1}{2}z for y in the equation z=8-3y.
z=2
Solve z=8-3\left(1+\frac{1}{2}z\right) for z.
y=1+\frac{1}{2}\times 2
Substitute 2 for z in the equation y=1+\frac{1}{2}z.
y=2
Calculate y from y=1+\frac{1}{2}\times 2.
x=-1+2
Substitute 2 for y in the equation x=-1+y.
x=1
Calculate x from x=-1+2.
x=1 y=2 z=2
The system is now solved.
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