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Solve for x, y, z
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5x-3y-z=1 1x-3y+4z=0 6x-3y+z=0
Reorder the equations.
z=5x-3y-1
Solve 5x-3y-z=1 for z.
1x-3y+4\left(5x-3y-1\right)=0 6x-3y+5x-3y-1=0
Substitute 5x-3y-1 for z in the second and third equation.
y=-\frac{4}{15}+\frac{7}{5}x x=\frac{6}{11}y+\frac{1}{11}
Solve these equations for y and x respectively.
x=\frac{6}{11}\left(-\frac{4}{15}+\frac{7}{5}x\right)+\frac{1}{11}
Substitute -\frac{4}{15}+\frac{7}{5}x for y in the equation x=\frac{6}{11}y+\frac{1}{11}.
x=-\frac{3}{13}
Solve x=\frac{6}{11}\left(-\frac{4}{15}+\frac{7}{5}x\right)+\frac{1}{11} for x.
y=-\frac{4}{15}+\frac{7}{5}\left(-\frac{3}{13}\right)
Substitute -\frac{3}{13} for x in the equation y=-\frac{4}{15}+\frac{7}{5}x.
y=-\frac{23}{39}
Calculate y from y=-\frac{4}{15}+\frac{7}{5}\left(-\frac{3}{13}\right).
z=5\left(-\frac{3}{13}\right)-3\left(-\frac{23}{39}\right)-1
Substitute -\frac{23}{39} for y and -\frac{3}{13} for x in the equation z=5x-3y-1.
z=-\frac{5}{13}
Calculate z from z=5\left(-\frac{3}{13}\right)-3\left(-\frac{23}{39}\right)-1.
x=-\frac{3}{13} y=-\frac{23}{39} z=-\frac{5}{13}
The system is now solved.