Solve for x, y, z
x=1
y=2
z=3
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x=-4y+z+6
Solve x+4y-z=6 for x.
2\left(-4y+z+6\right)+5y-7z=-9 3\left(-4y+z+6\right)-2y+z=2
Substitute -4y+z+6 for x in the second and third equation.
y=-\frac{5}{3}z+7 z=-4+\frac{7}{2}y
Solve these equations for y and z respectively.
z=-4+\frac{7}{2}\left(-\frac{5}{3}z+7\right)
Substitute -\frac{5}{3}z+7 for y in the equation z=-4+\frac{7}{2}y.
z=3
Solve z=-4+\frac{7}{2}\left(-\frac{5}{3}z+7\right) for z.
y=-\frac{5}{3}\times 3+7
Substitute 3 for z in the equation y=-\frac{5}{3}z+7.
y=2
Calculate y from y=-\frac{5}{3}\times 3+7.
x=-4\times 2+3+6
Substitute 2 for y and 3 for z in the equation x=-4y+z+6.
x=1
Calculate x from x=-4\times 2+3+6.
x=1 y=2 z=3
The system is now solved.
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