Solve for x, y, z
x=1
y=2
z=3
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x=-y-2z+9
Solve x+y+2z=9 for x.
2\left(-y-2z+9\right)+4y-3z=1 3\left(-y-2z+9\right)+6y-5z=0
Substitute -y-2z+9 for x in the second and third equation.
y=\frac{7}{2}z-\frac{17}{2} z=\frac{27}{11}+\frac{3}{11}y
Solve these equations for y and z respectively.
z=\frac{27}{11}+\frac{3}{11}\left(\frac{7}{2}z-\frac{17}{2}\right)
Substitute \frac{7}{2}z-\frac{17}{2} for y in the equation z=\frac{27}{11}+\frac{3}{11}y.
z=3
Solve z=\frac{27}{11}+\frac{3}{11}\left(\frac{7}{2}z-\frac{17}{2}\right) for z.
y=\frac{7}{2}\times 3-\frac{17}{2}
Substitute 3 for z in the equation y=\frac{7}{2}z-\frac{17}{2}.
y=2
Calculate y from y=\frac{7}{2}\times 3-\frac{17}{2}.
x=-2-2\times 3+9
Substitute 2 for y and 3 for z in the equation x=-y-2z+9.
x=1
Calculate x from x=-2-2\times 3+9.
x=1 y=2 z=3
The system is now solved.
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