Solve for x, y, z
x=-1
y=2
z=5
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2x+y+z=5 2x-3y+2z=2 2x+8y-3z=-1
Reorder the equations.
y=-2x-z+5
Solve 2x+y+z=5 for y.
2x-3\left(-2x-z+5\right)+2z=2 2x+8\left(-2x-z+5\right)-3z=-1
Substitute -2x-z+5 for y in the second and third equation.
x=-\frac{5}{8}z+\frac{17}{8} z=-\frac{14}{11}x+\frac{41}{11}
Solve these equations for x and z respectively.
z=-\frac{14}{11}\left(-\frac{5}{8}z+\frac{17}{8}\right)+\frac{41}{11}
Substitute -\frac{5}{8}z+\frac{17}{8} for x in the equation z=-\frac{14}{11}x+\frac{41}{11}.
z=5
Solve z=-\frac{14}{11}\left(-\frac{5}{8}z+\frac{17}{8}\right)+\frac{41}{11} for z.
x=-\frac{5}{8}\times 5+\frac{17}{8}
Substitute 5 for z in the equation x=-\frac{5}{8}z+\frac{17}{8}.
x=-1
Calculate x from x=-\frac{5}{8}\times 5+\frac{17}{8}.
y=-2\left(-1\right)-5+5
Substitute -1 for x and 5 for z in the equation y=-2x-z+5.
y=2
Calculate y from y=-2\left(-1\right)-5+5.
x=-1 y=2 z=5
The system is now solved.
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