Solve 5a+9b=3a+13b

$$5 a + 9 b = 3 a + 13 b$$

Solve for a

$$a=2b$$

Steps for Solving Linear Equation

Subtract 3a from both sides.

$$5a+9b-3a=13b$$

Combine 5a and -3a to get 2a.

$$2a+9b=13b$$

Subtract 9b from both sides.

$$2a=13b-9b$$

Combine 13b and -9b to get 4b.

$$2a=4b$$

Divide both sides by 2.

$$\frac{2a}{2}=\frac{4b}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$a=\frac{4b}{2}$$

Divide 4b by 2.

$$a=2b$$

Solve for b

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

Steps for Solving Linear Equation

Subtract 13b from both sides.

$$5a+9b-13b=3a$$

Combine 9b and -13b to get -4b.

$$5a-4b=3a$$

Subtract 5a from both sides.

$$-4b=3a-5a$$

Combine 3a and -5a to get -2a.

$$-4b=-2a$$

Divide both sides by -4.

$$\frac{-4b}{-4}=-\frac{2a}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$b=-\frac{2a}{-4}$$

Divide -2a by -4.

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