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)+4y+z=13 -\left(-y-z+6\right)-y+z=0
Substitute -y-z+6 for x in the second and third equation.
y=\frac{1}{2}+\frac{1}{2}z z=3
Solve these equations for y and z respectively.
y=\frac{1}{2}+\frac{1}{2}\times 3
Substitute 3 for z in the equation y=\frac{1}{2}+\frac{1}{2}z.
y=2
Calculate y from y=\frac{1}{2}+\frac{1}{2}\times 3.
x=-2-3+6
Substitute 2 for y and 3 for z 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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