Solve for a
a=\frac{3b}{10}
Solve for b
b=\frac{10a}{3}
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5a=6b-15a
Multiply both sides of the equation by 15, the least common multiple of 3,5.
5a+15a=6b
Add 15a to both sides.
20a=6b
Combine 5a and 15a to get 20a.
\frac{20a}{20}=\frac{6b}{20}
Divide both sides by 20.
a=\frac{6b}{20}
Dividing by 20 undoes the multiplication by 20.
a=\frac{3b}{10}
Divide 6b by 20.
5a=6b-15a
Multiply both sides of the equation by 15, the least common multiple of 3,5.
6b-15a=5a
Swap sides so that all variable terms are on the left hand side.
6b=5a+15a
Add 15a to both sides.
6b=20a
Combine 5a and 15a to get 20a.
\frac{6b}{6}=\frac{20a}{6}
Divide both sides by 6.
b=\frac{20a}{6}
Dividing by 6 undoes the multiplication by 6.
b=\frac{10a}{3}
Divide 20a by 6.
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