Solve for x, y, z
x=2
y=-3
z=4
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x+2y+3z=8 2x-5y+2z=27 5x+4y-5z=-22
Reorder the equations.
x=-2y-3z+8
Solve x+2y+3z=8 for x.
2\left(-2y-3z+8\right)-5y+2z=27 5\left(-2y-3z+8\right)+4y-5z=-22
Substitute -2y-3z+8 for x in the second and third equation.
y=-\frac{4}{9}z-\frac{11}{9} z=\frac{31}{10}-\frac{3}{10}y
Solve these equations for y and z respectively.
z=\frac{31}{10}-\frac{3}{10}\left(-\frac{4}{9}z-\frac{11}{9}\right)
Substitute -\frac{4}{9}z-\frac{11}{9} for y in the equation z=\frac{31}{10}-\frac{3}{10}y.
z=4
Solve z=\frac{31}{10}-\frac{3}{10}\left(-\frac{4}{9}z-\frac{11}{9}\right) for z.
y=-\frac{4}{9}\times 4-\frac{11}{9}
Substitute 4 for z in the equation y=-\frac{4}{9}z-\frac{11}{9}.
y=-3
Calculate y from y=-\frac{4}{9}\times 4-\frac{11}{9}.
x=-2\left(-3\right)-3\times 4+8
Substitute -3 for y and 4 for z in the equation x=-2y-3z+8.
x=2
Calculate x from x=-2\left(-3\right)-3\times 4+8.
x=2 y=-3 z=4
The system is now solved.
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