Solve for x
x=-\frac{5z}{3}
Solve for z
z=-\frac{3x}{5}
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3\left(x-z\right)=6x+2z
Multiply both sides of the equation by 6, the least common multiple of 2,3.
3x-3z=6x+2z
Use the distributive property to multiply 3 by x-z.
3x-3z-6x=2z
Subtract 6x from both sides.
-3x-3z=2z
Combine 3x and -6x to get -3x.
-3x=2z+3z
Add 3z to both sides.
-3x=5z
Combine 2z and 3z to get 5z.
\frac{-3x}{-3}=\frac{5z}{-3}
Divide both sides by -3.
x=\frac{5z}{-3}
Dividing by -3 undoes the multiplication by -3.
x=-\frac{5z}{3}
Divide 5z by -3.
3\left(x-z\right)=6x+2z
Multiply both sides of the equation by 6, the least common multiple of 2,3.
3x-3z=6x+2z
Use the distributive property to multiply 3 by x-z.
3x-3z-2z=6x
Subtract 2z from both sides.
3x-5z=6x
Combine -3z and -2z to get -5z.
-5z=6x-3x
Subtract 3x from both sides.
-5z=3x
Combine 6x and -3x to get 3x.
\frac{-5z}{-5}=\frac{3x}{-5}
Divide both sides by -5.
z=\frac{3x}{-5}
Dividing by -5 undoes the multiplication by -5.
z=-\frac{3x}{5}
Divide 3x by -5.
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