\left\{ \begin{array} { l } { 3 x - y = - 17 } \\ { x + 3 z = - 5 } \\ { 2 y - z = 4 } \end{array} \right.
Solve for x, y, z
x=-5
y=2
z=0
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y=3x+17
Solve 3x-y=-17 for y.
2\left(3x+17\right)-z=4
Substitute 3x+17 for y in the equation 2y-z=4.
x=-3z-5 z=30+6x
Solve the second equation for x and the third equation for z.
z=30+6\left(-3z-5\right)
Substitute -3z-5 for x in the equation z=30+6x.
z=0
Solve z=30+6\left(-3z-5\right) for z.
x=-3\times 0-5
Substitute 0 for z in the equation x=-3z-5.
x=-5
Calculate x from x=-3\times 0-5.
y=3\left(-5\right)+17
Substitute -5 for x in the equation y=3x+17.
y=2
Calculate y from y=3\left(-5\right)+17.
x=-5 y=2 z=0
The system is now solved.
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