Solve for x, y, z
x=2
y=1
z=1
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x+y-7z=-4 4x+5y-7z=6 2x+3y+4z=11
Reorder the equations.
x=-y+7z-4
Solve x+y-7z=-4 for x.
4\left(-y+7z-4\right)+5y-7z=6 2\left(-y+7z-4\right)+3y+4z=11
Substitute -y+7z-4 for x in the second and third equation.
y=-21z+22 z=-\frac{1}{18}y+\frac{19}{18}
Solve these equations for y and z respectively.
z=-\frac{1}{18}\left(-21z+22\right)+\frac{19}{18}
Substitute -21z+22 for y in the equation z=-\frac{1}{18}y+\frac{19}{18}.
z=1
Solve z=-\frac{1}{18}\left(-21z+22\right)+\frac{19}{18} for z.
y=-21+22
Substitute 1 for z in the equation y=-21z+22.
y=1
Calculate y from y=-21+22.
x=-1+7\times 1-4
Substitute 1 for y and 1 for z in the equation x=-y+7z-4.
x=2
Calculate x from x=-1+7\times 1-4.
x=2 y=1 z=1
The system is now solved.
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