\left\{ \begin{array}{l}{ x - y = 2 }\\{ 4 x - 6 z = 16 }\\{ 4 y + z = 8 }\end{array} \right.
Solve for x, y, z
x=4
y=2
z=0
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x=y+2
Solve x-y=2 for x.
4\left(y+2\right)-6z=16
Substitute y+2 for x in the equation 4x-6z=16.
y=2+\frac{3}{2}z z=8-4y
Solve the second equation for y and the third equation for z.
z=8-4\left(2+\frac{3}{2}z\right)
Substitute 2+\frac{3}{2}z for y in the equation z=8-4y.
z=0
Solve z=8-4\left(2+\frac{3}{2}z\right) for z.
y=2+\frac{3}{2}\times 0
Substitute 0 for z in the equation y=2+\frac{3}{2}z.
y=2
Calculate y from y=2+\frac{3}{2}\times 0.
x=2+2
Substitute 2 for y in the equation x=y+2.
x=4
Calculate x from x=2+2.
x=4 y=2 z=0
The system is now solved.
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