Solve {l}{3a=10}{a+2b=20}{b+4c=9}

$$\left. \begin{array} { l } { 3 a = 10 } \\ { a + 2 b = 20 } \\ { b + 4 c = 9 } \end{array} \right.$$

Solve for a, b, c

$$a = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

$$b = \frac{25}{3} = 8\frac{1}{3} \approx 8.333333333$$

$$c=\frac{1}{6}\approx 0.166666667$$

Solution Steps

Consider the first equation. Divide both sides by 3.

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

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

$$\frac{10}{3}+2b=20$$

Subtract \frac{10}{3} from both sides.

$$2b=20-\frac{10}{3}$$

Subtract \frac{10}{3} from 20 to get \frac{50}{3}.

$$2b=\frac{50}{3}$$

Divide both sides by 2.

$$b=\frac{\frac{50}{3}}{2}$$

Express \frac{\frac{50}{3}}{2} as a single fraction.

$$b=\frac{50}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$b=\frac{50}{6}$$

Reduce the fraction \frac{50}{6} to lowest terms by extracting and canceling out 2.

$$b=\frac{25}{3}$$

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

$$\frac{25}{3}+4c=9$$

Subtract \frac{25}{3} from both sides.

$$4c=9-\frac{25}{3}$$

Subtract \frac{25}{3} from 9 to get \frac{2}{3}.

$$4c=\frac{2}{3}$$

Divide both sides by 4.

$$c=\frac{\frac{2}{3}}{4}$$

Express \frac{\frac{2}{3}}{4} as a single fraction.

$$c=\frac{2}{3\times 4}$$

Multiply 3 and 4 to get 12.

$$c=\frac{2}{12}$$

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

$$c=\frac{1}{6}$$

The system is now solved.

$$a=\frac{10}{3} b=\frac{25}{3} c=\frac{1}{6}$$