Solve for x, y, z
x=2
y=3
z=4
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x+y+z=9 3x+2y=12 2x+3y=13
Reorder the equations.
x=-y-z+9
Solve x+y+z=9 for x.
3\left(-y-z+9\right)+2y=12 2\left(-y-z+9\right)+3y=13
Substitute -y-z+9 for x in the second and third equation.
y=-3z+15 z=\frac{5}{2}+\frac{1}{2}y
Solve these equations for y and z respectively.
z=\frac{5}{2}+\frac{1}{2}\left(-3z+15\right)
Substitute -3z+15 for y in the equation z=\frac{5}{2}+\frac{1}{2}y.
z=4
Solve z=\frac{5}{2}+\frac{1}{2}\left(-3z+15\right) for z.
y=-3\times 4+15
Substitute 4 for z in the equation y=-3z+15.
y=3
Calculate y from y=-3\times 4+15.
x=-3-4+9
Substitute 3 for y and 4 for z in the equation x=-y-z+9.
x=2
Calculate x from x=-3-4+9.
x=2 y=3 z=4
The system is now solved.
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