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Solve for x, y, z
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x=y+5
Solve x-y=5 for x.
-\left(y+5\right)+4y+2z=3 -\left(y+5\right)+3y-5z=-6
Substitute y+5 for x in the second and third equation.
y=\frac{8}{3}-\frac{2}{3}z z=\frac{2}{5}y+\frac{1}{5}
Solve these equations for y and z respectively.
z=\frac{2}{5}\left(\frac{8}{3}-\frac{2}{3}z\right)+\frac{1}{5}
Substitute \frac{8}{3}-\frac{2}{3}z for y in the equation z=\frac{2}{5}y+\frac{1}{5}.
z=1
Solve z=\frac{2}{5}\left(\frac{8}{3}-\frac{2}{3}z\right)+\frac{1}{5} for z.
y=\frac{8}{3}-\frac{2}{3}
Substitute 1 for z in the equation y=\frac{8}{3}-\frac{2}{3}z.
y=2
Calculate y from y=\frac{8}{3}-\frac{2}{3}.
x=2+5
Substitute 2 for y in the equation x=y+5.
x=7
Calculate x from x=2+5.
x=7 y=2 z=1
The system is now solved.