\left\{ \begin{array} { l } { 2 x + y = 2 } \\ { - 3 x + z = - 7 } \\ { - 4 y + 3 z = 22 } \end{array} \right.
Solve for x, y, z
x=3
y=-4
z=2
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y=2-2x
Solve 2x+y=2 for y.
-4\left(2-2x\right)+3z=22
Substitute 2-2x for y in the equation -4y+3z=22.
x=\frac{7}{3}+\frac{1}{3}z z=10-\frac{8}{3}x
Solve the second equation for x and the third equation for z.
z=10-\frac{8}{3}\left(\frac{7}{3}+\frac{1}{3}z\right)
Substitute \frac{7}{3}+\frac{1}{3}z for x in the equation z=10-\frac{8}{3}x.
z=2
Solve z=10-\frac{8}{3}\left(\frac{7}{3}+\frac{1}{3}z\right) for z.
x=\frac{7}{3}+\frac{1}{3}\times 2
Substitute 2 for z in the equation x=\frac{7}{3}+\frac{1}{3}z.
x=3
Calculate x from x=\frac{7}{3}+\frac{1}{3}\times 2.
y=2-2\times 3
Substitute 3 for x in the equation y=2-2x.
y=-4
Calculate y from y=2-2\times 3.
x=3 y=-4 z=2
The system is now solved.
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