Solve for a
a=\frac{5-3b}{2}
Solve for b
b=\frac{5-2a}{3}
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2\left(a+2\right)+3\left(b-1\right)=6
Multiply both sides of the equation by 6, the least common multiple of 3,2.
2a+4+3\left(b-1\right)=6
Use the distributive property to multiply 2 by a+2.
2a+4+3b-3=6
Use the distributive property to multiply 3 by b-1.
2a+1+3b=6
Subtract 3 from 4 to get 1.
2a+3b=6-1
Subtract 1 from both sides.
2a+3b=5
Subtract 1 from 6 to get 5.
2a=5-3b
Subtract 3b from both sides.
\frac{2a}{2}=\frac{5-3b}{2}
Divide both sides by 2.
a=\frac{5-3b}{2}
Dividing by 2 undoes the multiplication by 2.
2\left(a+2\right)+3\left(b-1\right)=6
Multiply both sides of the equation by 6, the least common multiple of 3,2.
2a+4+3\left(b-1\right)=6
Use the distributive property to multiply 2 by a+2.
2a+4+3b-3=6
Use the distributive property to multiply 3 by b-1.
2a+1+3b=6
Subtract 3 from 4 to get 1.
1+3b=6-2a
Subtract 2a from both sides.
3b=6-2a-1
Subtract 1 from both sides.
3b=5-2a
Subtract 1 from 6 to get 5.
\frac{3b}{3}=\frac{5-2a}{3}
Divide both sides by 3.
b=\frac{5-2a}{3}
Dividing by 3 undoes the multiplication by 3.
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