Solve 2a+3b=10ab

$$2 a + 3 b = 10 a b$$

Solve for a

$$a=-\frac{3b}{2\left(1-5b\right)}$$

$$b\neq \frac{1}{5}$$

Steps for Solving Linear Equation

Subtract 10ab from both sides.

$$2a+3b-10ab=0$$

Subtract 3b from both sides. Anything subtracted from zero gives its negation.

$$2a-10ab=-3b$$

Combine all terms containing a.

$$\left(2-10b\right)a=-3b$$

Divide both sides by 2-10b.

$$\frac{\left(2-10b\right)a}{2-10b}=-\frac{3b}{2-10b}$$

Dividing by 2-10b undoes the multiplication by 2-10b.

$$a=-\frac{3b}{2-10b}$$

Divide -3b by 2-10b.

$$a=-\frac{3b}{2\left(1-5b\right)}$$

Solve for b

$$b=-\frac{2a}{3-10a}$$

$$a\neq \frac{3}{10}$$

Steps for Solving Linear Equation

Subtract 10ab from both sides.

$$2a+3b-10ab=0$$

Subtract 2a from both sides. Anything subtracted from zero gives its negation.

$$3b-10ab=-2a$$

Combine all terms containing b.

$$\left(3-10a\right)b=-2a$$

Divide both sides by 3-10a.

$$\frac{\left(3-10a\right)b}{3-10a}=-\frac{2a}{3-10a}$$

Dividing by 3-10a undoes the multiplication by 3-10a.

$$b=-\frac{2a}{3-10a}$$