Solve for x, y, z
x=18-a
y=a-12
z=a
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z=2x+3y x+y=6 a=z
Reorder the equations.
a=2x+3y
Substitute 2x+3y for z in the equation a=z.
y=-x+6 x=\frac{1}{2}a-\frac{3}{2}y
Solve the second equation for y and the third equation for x.
x=\frac{1}{2}a-\frac{3}{2}\left(-x+6\right)
Substitute -x+6 for y in the equation x=\frac{1}{2}a-\frac{3}{2}y.
x=18-a
Solve x=\frac{1}{2}a-\frac{3}{2}\left(-x+6\right) for x.
y=-\left(18-a\right)+6
Substitute 18-a for x in the equation y=-x+6.
y=-12+a
Calculate y from y=-\left(18-a\right)+6.
z=2\left(18-a\right)+3\left(-12+a\right)
Substitute -12+a for y and 18-a for x in the equation z=2x+3y.
z=a
Calculate z from z=2\left(18-a\right)+3\left(-12+a\right).
x=18-a y=-12+a z=a
The system is now solved.
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