\left\{ \begin{array} { l } { x + y + z = 3 } \\ { 3 x + y - 2 z = - 23 } \\ { - 2 x - 3 y + 2 z = 17 } \end{array} \right.
Solve for x, y, z
x=-4
y=1
z=6
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x=-y-z+3
Solve x+y+z=3 for x.
3\left(-y-z+3\right)+y-2z=-23 -2\left(-y-z+3\right)-3y+2z=17
Substitute -y-z+3 for x in the second and third equation.
y=-\frac{5}{2}z+16 z=\frac{23}{4}+\frac{1}{4}y
Solve these equations for y and z respectively.
z=\frac{23}{4}+\frac{1}{4}\left(-\frac{5}{2}z+16\right)
Substitute -\frac{5}{2}z+16 for y in the equation z=\frac{23}{4}+\frac{1}{4}y.
z=6
Solve z=\frac{23}{4}+\frac{1}{4}\left(-\frac{5}{2}z+16\right) for z.
y=-\frac{5}{2}\times 6+16
Substitute 6 for z in the equation y=-\frac{5}{2}z+16.
y=1
Calculate y from y=-\frac{5}{2}\times 6+16.
x=-1-6+3
Substitute 1 for y and 6 for z in the equation x=-y-z+3.
x=-4
Calculate x from x=-1-6+3.
x=-4 y=1 z=6
The system is now solved.
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