Solve for a
a=\frac{6b}{5}-3
Solve for b
b=\frac{5\left(a+3\right)}{6}
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5a=6b-15
Multiply both sides of the equation by 15, the least common multiple of 3,5.
\frac{5a}{5}=\frac{6b-15}{5}
Divide both sides by 5.
a=\frac{6b-15}{5}
Dividing by 5 undoes the multiplication by 5.
a=\frac{6b}{5}-3
Divide 6b-15 by 5.
5a=6b-15
Multiply both sides of the equation by 15, the least common multiple of 3,5.
6b-15=5a
Swap sides so that all variable terms are on the left hand side.
6b=5a+15
Add 15 to both sides.
\frac{6b}{6}=\frac{5a+15}{6}
Divide both sides by 6.
b=\frac{5a+15}{6}
Dividing by 6 undoes the multiplication by 6.
b=\frac{5a}{6}+\frac{5}{2}
Divide 15+5a by 6.
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