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