Solve {l}{c+b=6}{b+9b=12}

$$\left\{ \begin{array} { l } { c + b = 6 } \\ { b + 9 b = 12 } \end{array} \right.$$

Solve for c, b

$$c = \frac{24}{5} = 4\frac{4}{5} = 4.8$$

$$b = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

Solution Steps

Consider the second equation. Combine b and 9b to get 10b.

$$10b=12$$

Divide both sides by 10.

$$b=\frac{12}{10}$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$b=\frac{6}{5}$$

Consider the first equation. Insert the known values of variables into the equation.

$$c+\frac{6}{5}=6$$

Subtract \frac{6}{5} from both sides.

$$c=6-\frac{6}{5}$$

Subtract \frac{6}{5} from 6 to get \frac{24}{5}.

$$c=\frac{24}{5}$$

The system is now solved.

$$c=\frac{24}{5} b=\frac{6}{5}$$