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Solve for x, y, z
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z=3x-4y 6x-7y=1 a=z
Reorder the equations.
a=3x-4y
Substitute 3x-4y for z in the equation a=z.
y=\frac{6}{7}x-\frac{1}{7} x=\frac{1}{3}a+\frac{4}{3}y
Solve the second equation for y and the third equation for x.
x=\frac{1}{3}a+\frac{4}{3}\left(\frac{6}{7}x-\frac{1}{7}\right)
Substitute \frac{6}{7}x-\frac{1}{7} for y in the equation x=\frac{1}{3}a+\frac{4}{3}y.
x=\frac{4}{3}-\frac{7}{3}a
Solve x=\frac{1}{3}a+\frac{4}{3}\left(\frac{6}{7}x-\frac{1}{7}\right) for x.
y=\frac{6}{7}\left(\frac{4}{3}-\frac{7}{3}a\right)-\frac{1}{7}
Substitute \frac{4}{3}-\frac{7}{3}a for x in the equation y=\frac{6}{7}x-\frac{1}{7}.
y=1-2a
Calculate y from y=\frac{6}{7}\left(\frac{4}{3}-\frac{7}{3}a\right)-\frac{1}{7}.
z=3\left(\frac{4}{3}-\frac{7}{3}a\right)-4\left(1-2a\right)
Substitute 1-2a for y and \frac{4}{3}-\frac{7}{3}a for x in the equation z=3x-4y.
z=a
Calculate z from z=3\left(\frac{4}{3}-\frac{7}{3}a\right)-4\left(1-2a\right).
x=\frac{4}{3}-\frac{7}{3}a y=1-2a z=a
The system is now solved.