\left\{ \begin{array} { l } { - 2 y + z = 7 } \\ { x + 4 y = - 14 } \\ { 3 x - 2 z = - 8 } \end{array} \right.
Solve for y, z, x
x=-2
y=-3
z=1
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z=2y+7
Solve -2y+z=7 for z.
3x-2\left(2y+7\right)=-8
Substitute 2y+7 for z in the equation 3x-2z=-8.
y=-\frac{1}{4}x-\frac{7}{2} x=2+\frac{4}{3}y
Solve the second equation for y and the third equation for x.
x=2+\frac{4}{3}\left(-\frac{1}{4}x-\frac{7}{2}\right)
Substitute -\frac{1}{4}x-\frac{7}{2} for y in the equation x=2+\frac{4}{3}y.
x=-2
Solve x=2+\frac{4}{3}\left(-\frac{1}{4}x-\frac{7}{2}\right) for x.
y=-\frac{1}{4}\left(-2\right)-\frac{7}{2}
Substitute -2 for x in the equation y=-\frac{1}{4}x-\frac{7}{2}.
y=-3
Calculate y from y=-\frac{1}{4}\left(-2\right)-\frac{7}{2}.
z=2\left(-3\right)+7
Substitute -3 for y in the equation z=2y+7.
z=1
Calculate z from z=2\left(-3\right)+7.
y=-3 z=1 x=-2
The system is now solved.
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