Solve for x
x=\frac{30z}{7}-\frac{6y}{7}+4
Solve for y
y=-\frac{7x}{6}+5z+\frac{14}{3}
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6\left(y-5z\right)=-7\left(x-4\right)
Multiply both sides of the equation by 6.
6y-30z=-7\left(x-4\right)
Use the distributive property to multiply 6 by y-5z.
6y-30z=-7x+28
Use the distributive property to multiply -7 by x-4.
-7x+28=6y-30z
Swap sides so that all variable terms are on the left hand side.
-7x=6y-30z-28
Subtract 28 from both sides.
\frac{-7x}{-7}=\frac{6y-30z-28}{-7}
Divide both sides by -7.
x=\frac{6y-30z-28}{-7}
Dividing by -7 undoes the multiplication by -7.
x=\frac{30z}{7}-\frac{6y}{7}+4
Divide 6y-30z-28 by -7.
6\left(y-5z\right)=-7\left(x-4\right)
Multiply both sides of the equation by 6.
6y-30z=-7\left(x-4\right)
Use the distributive property to multiply 6 by y-5z.
6y-30z=-7x+28
Use the distributive property to multiply -7 by x-4.
6y=-7x+28+30z
Add 30z to both sides.
6y=28+30z-7x
The equation is in standard form.
\frac{6y}{6}=\frac{28+30z-7x}{6}
Divide both sides by 6.
y=\frac{28+30z-7x}{6}
Dividing by 6 undoes the multiplication by 6.
y=-\frac{7x}{6}+5z+\frac{14}{3}
Divide -7x+28+30z by 6.
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