Solve for x, y, z
x=15
y=20
z=10
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x=-2y-3z+85
Solve x+2y+3z=85 for x.
3\left(-2y-3z+85\right)+2y+2z=105 2\left(-2y-3z+85\right)+3y+2z=110
Substitute -2y-3z+85 for x in the second and third equation.
y=-\frac{7}{4}z+\frac{75}{2} z=-\frac{1}{4}y+15
Solve these equations for y and z respectively.
z=-\frac{1}{4}\left(-\frac{7}{4}z+\frac{75}{2}\right)+15
Substitute -\frac{7}{4}z+\frac{75}{2} for y in the equation z=-\frac{1}{4}y+15.
z=10
Solve z=-\frac{1}{4}\left(-\frac{7}{4}z+\frac{75}{2}\right)+15 for z.
y=-\frac{7}{4}\times 10+\frac{75}{2}
Substitute 10 for z in the equation y=-\frac{7}{4}z+\frac{75}{2}.
y=20
Calculate y from y=-\frac{7}{4}\times 10+\frac{75}{2}.
x=-2\times 20-3\times 10+85
Substitute 20 for y and 10 for z in the equation x=-2y-3z+85.
x=15
Calculate x from x=-2\times 20-3\times 10+85.
x=15 y=20 z=10
The system is now solved.
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