Solve for x, y, z
x=2
y=-1
z=3
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x=y-2z+9
Solve x-y+2z=9 for x.
2\left(y-2z+9\right)-5y+3z=18 6\left(y-2z+9\right)+7y+10z=35
Substitute y-2z+9 for x in the second and third equation.
y=-\frac{1}{3}z z=\frac{13}{2}y+\frac{19}{2}
Solve these equations for y and z respectively.
z=\frac{13}{2}\left(-\frac{1}{3}\right)z+\frac{19}{2}
Substitute -\frac{1}{3}z for y in the equation z=\frac{13}{2}y+\frac{19}{2}.
z=3
Solve z=\frac{13}{2}\left(-\frac{1}{3}\right)z+\frac{19}{2} for z.
y=-\frac{1}{3}\times 3
Substitute 3 for z in the equation y=-\frac{1}{3}z.
y=-1
Calculate y from y=-\frac{1}{3}\times 3.
x=-1-2\times 3+9
Substitute -1 for y and 3 for z in the equation x=y-2z+9.
x=2
Calculate x from x=-1-2\times 3+9.
x=2 y=-1 z=3
The system is now solved.
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