Solve for x, y, z
x=4
y=1
z=3
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x+5y+3z=18 3x+2y-4z=2 5x-7y-5z=-2
Reorder the equations.
x=-5y-3z+18
Solve x+5y+3z=18 for x.
3\left(-5y-3z+18\right)+2y-4z=2 5\left(-5y-3z+18\right)-7y-5z=-2
Substitute -5y-3z+18 for x in the second and third equation.
y=4-z z=\frac{23}{5}-\frac{8}{5}y
Solve these equations for y and z respectively.
z=\frac{23}{5}-\frac{8}{5}\left(4-z\right)
Substitute 4-z for y in the equation z=\frac{23}{5}-\frac{8}{5}y.
z=3
Solve z=\frac{23}{5}-\frac{8}{5}\left(4-z\right) for z.
y=4-3
Substitute 3 for z in the equation y=4-z.
y=1
Calculate y from y=4-3.
x=-5-3\times 3+18
Substitute 1 for y and 3 for z in the equation x=-5y-3z+18.
x=4
Calculate x from x=-5-3\times 3+18.
x=4 y=1 z=3
The system is now solved.
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