Solve for x, y, z
x=4
y=5
z=1
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x=y-3z+2
Solve x-y+3z=2 for x.
2\left(y-3z+2\right)+y-5z=8 y-3z+2-2y+7z=1
Substitute y-3z+2 for x in the second and third equation.
y=\frac{11}{3}z+\frac{4}{3} z=-\frac{1}{4}+\frac{1}{4}y
Solve these equations for y and z respectively.
z=-\frac{1}{4}+\frac{1}{4}\left(\frac{11}{3}z+\frac{4}{3}\right)
Substitute \frac{11}{3}z+\frac{4}{3} for y in the equation z=-\frac{1}{4}+\frac{1}{4}y.
z=1
Solve z=-\frac{1}{4}+\frac{1}{4}\left(\frac{11}{3}z+\frac{4}{3}\right) for z.
y=\frac{11}{3}\times 1+\frac{4}{3}
Substitute 1 for z in the equation y=\frac{11}{3}z+\frac{4}{3}.
y=5
Calculate y from y=\frac{11}{3}\times 1+\frac{4}{3}.
x=5-3+2
Substitute 5 for y and 1 for z in the equation x=y-3z+2.
x=4
Calculate x from x=5-3+2.
x=4 y=5 z=1
The system is now solved.
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