Solve for a
a=-\frac{7b}{b-7}
b\neq 7
Solve for b
b=\frac{7a}{a+7}
a\neq -7
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ab=7a-7b
Use the distributive property to multiply 7 by a-b.
ab-7a=-7b
Subtract 7a from both sides.
\left(b-7\right)a=-7b
Combine all terms containing a.
\frac{\left(b-7\right)a}{b-7}=-\frac{7b}{b-7}
Divide both sides by b-7.
a=-\frac{7b}{b-7}
Dividing by b-7 undoes the multiplication by b-7.
ab=7a-7b
Use the distributive property to multiply 7 by a-b.
ab+7b=7a
Add 7b to both sides.
\left(a+7\right)b=7a
Combine all terms containing b.
\frac{\left(a+7\right)b}{a+7}=\frac{7a}{a+7}
Divide both sides by a+7.
b=\frac{7a}{a+7}
Dividing by a+7 undoes the multiplication by a+7.
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