Solve for x, y, z
x=-1
y=-1
z=-1
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x-3y+z=1 4x-5y-11z=12 2x+3y-7z=2
Reorder the equations.
x=3y-z+1
Solve x-3y+z=1 for x.
4\left(3y-z+1\right)-5y-11z=12 2\left(3y-z+1\right)+3y-7z=2
Substitute 3y-z+1 for x in the second and third equation.
y=\frac{15}{7}z+\frac{8}{7} z=y
Solve these equations for y and z respectively.
z=\frac{15}{7}z+\frac{8}{7}
Substitute \frac{15}{7}z+\frac{8}{7} for y in the equation z=y.
z=-1
Solve z=\frac{15}{7}z+\frac{8}{7} for z.
y=\frac{15}{7}\left(-1\right)+\frac{8}{7}
Substitute -1 for z in the equation y=\frac{15}{7}z+\frac{8}{7}.
y=-1
Calculate y from y=\frac{15}{7}\left(-1\right)+\frac{8}{7}.
x=3\left(-1\right)-\left(-1\right)+1
Substitute -1 for y and -1 for z in the equation x=3y-z+1.
x=-1
Calculate x from x=3\left(-1\right)-\left(-1\right)+1.
x=-1 y=-1 z=-1
The system is now solved.
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