Solve 6a+3b=10a+30

$$6 a + 3 b = 10 a + 30$$

Solve for a

$$a=\frac{3\left(b-10\right)}{4}$$

Steps for Solving Linear Equation

Subtract 10a from both sides.

$$6a+3b-10a=30$$

Combine 6a and -10a to get -4a.

$$-4a+3b=30$$

Subtract 3b from both sides.

$$-4a=30-3b$$

Divide both sides by -4.

$$\frac{-4a}{-4}=\frac{30-3b}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$a=\frac{30-3b}{-4}$$

Divide 30-3b by -4.

$$a=\frac{3b}{4}-\frac{15}{2}$$

Solve for b

$$b=\frac{4a}{3}+10$$

Steps for Solving Linear Equation

Subtract 6a from both sides.

$$3b=10a+30-6a$$

Combine 10a and -6a to get 4a.

$$3b=4a+30$$

Divide both sides by 3.

$$\frac{3b}{3}=\frac{4a+30}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$b=\frac{4a+30}{3}$$

Divide 4a+30 by 3.

$$b=\frac{4a}{3}+10$$