Solve for x, y, z
x=1
y=2
z=3
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y=2x+3z-9
Solve 2x-y+3z=9 for y.
x+2x+3z-9+z=6 x-\left(2x+3z-9\right)+z=2
Substitute 2x+3z-9 for y in the second and third equation.
x=-\frac{4}{3}z+5 z=-\frac{1}{2}x+\frac{7}{2}
Solve these equations for x and z respectively.
z=-\frac{1}{2}\left(-\frac{4}{3}z+5\right)+\frac{7}{2}
Substitute -\frac{4}{3}z+5 for x in the equation z=-\frac{1}{2}x+\frac{7}{2}.
z=3
Solve z=-\frac{1}{2}\left(-\frac{4}{3}z+5\right)+\frac{7}{2} for z.
x=-\frac{4}{3}\times 3+5
Substitute 3 for z in the equation x=-\frac{4}{3}z+5.
x=1
Calculate x from x=-\frac{4}{3}\times 3+5.
y=2\times 1+3\times 3-9
Substitute 1 for x and 3 for z in the equation y=2x+3z-9.
y=2
Calculate y from y=2\times 1+3\times 3-9.
x=1 y=2 z=3
The system is now solved.
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