\left\{ \begin{array} { l } { 2 x + 3 y - z = 18 } \\ { 3 x - 2 y + z = 8 } \\ { x + 2 y + z = 24 } \end{array} \right.
Solve for x, y, z
x=4
y=6
z=8
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z=2x+3y-18
Solve 2x+3y-z=18 for z.
3x-2y+2x+3y-18=8 x+2y+2x+3y-18=24
Substitute 2x+3y-18 for z in the second and third equation.
y=-5x+26 x=-\frac{5}{3}y+14
Solve these equations for y and x respectively.
x=-\frac{5}{3}\left(-5x+26\right)+14
Substitute -5x+26 for y in the equation x=-\frac{5}{3}y+14.
x=4
Solve x=-\frac{5}{3}\left(-5x+26\right)+14 for x.
y=-5\times 4+26
Substitute 4 for x in the equation y=-5x+26.
y=6
Calculate y from y=-5\times 4+26.
z=2\times 4+3\times 6-18
Substitute 6 for y and 4 for x in the equation z=2x+3y-18.
z=8
Calculate z from z=2\times 4+3\times 6-18.
x=4 y=6 z=8
The system is now solved.
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