Solve {l}{2a+b=6}{b*3=10}

$$\left. \begin{array} { l } { 2 a + b = 6 } \\ { b \times 3 = 10 } \end{array} \right.$$

Solve for a, b

$$a = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

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

Solution Steps

Consider the second equation. Divide both sides by 3.

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

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

$$2a+\frac{10}{3}=6$$

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

$$2a=6-\frac{10}{3}$$

Subtract \frac{10}{3} from 6 to get \frac{8}{3}.

$$2a=\frac{8}{3}$$

Divide both sides by 2.

$$a=\frac{\frac{8}{3}}{2}$$

Express \frac{\frac{8}{3}}{2} as a single fraction.

$$a=\frac{8}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$a=\frac{8}{6}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$a=\frac{4}{3}$$

The system is now solved.

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