Solve 2ab-a+3b-3=-1

$$2 a b - a + 3 b - 3 = - 1$$

Solve for a

$$a=-\frac{3b-2}{2b-1}$$

$$b\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Subtract 3b from both sides.

$$2ab-a-3=-1-3b$$

Add 3 to both sides.

$$2ab-a=-1-3b+3$$

Add -1 and 3 to get 2.

$$2ab-a=2-3b$$

Combine all terms containing a.

$$\left(2b-1\right)a=2-3b$$

Divide both sides by 2b-1.

$$\frac{\left(2b-1\right)a}{2b-1}=\frac{2-3b}{2b-1}$$

Dividing by 2b-1 undoes the multiplication by 2b-1.

$$a=\frac{2-3b}{2b-1}$$

Solve for b

$$b=\frac{a+2}{2a+3}$$

$$a\neq -\frac{3}{2}$$

Steps for Solving Linear Equation

Add a to both sides.

$$2ab+3b-3=-1+a$$

Add 3 to both sides.

$$2ab+3b=-1+a+3$$

Add -1 and 3 to get 2.

$$2ab+3b=2+a$$

Combine all terms containing b.

$$\left(2a+3\right)b=2+a$$

The equation is in standard form.

$$\left(2a+3\right)b=a+2$$

Divide both sides by 2a+3.

$$\frac{\left(2a+3\right)b}{2a+3}=\frac{a+2}{2a+3}$$

Dividing by 2a+3 undoes the multiplication by 2a+3.

$$b=\frac{a+2}{2a+3}$$