Solve {l}{5x+1=8}{3x+7y=16}

$$\left\{ \begin{array} { l } { 5 x + 1 = 8 } \\ { 3 x + 7 y = 16 } \end{array} \right.$$

Solve for x, y

$$x = \frac{7}{5} = 1\frac{2}{5} = 1.4$$

$$y = \frac{59}{35} = 1\frac{24}{35} \approx 1.685714286$$

Solution Steps

Consider the first equation. Subtract 1 from both sides.

$$5x=8-1$$

Subtract 1 from 8 to get 7.

$$5x=7$$

Divide both sides by 5.

$$x=\frac{7}{5}$$

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

$$3\times \frac{7}{5}+7y=16$$

Multiply 3 and \frac{7}{5} to get \frac{21}{5}.

$$\frac{21}{5}+7y=16$$

Subtract \frac{21}{5} from both sides.

$$7y=16-\frac{21}{5}$$

Subtract \frac{21}{5} from 16 to get \frac{59}{5}.

$$7y=\frac{59}{5}$$

Divide both sides by 7.

$$y=\frac{\frac{59}{5}}{7}$$

Express \frac{\frac{59}{5}}{7} as a single fraction.

$$y=\frac{59}{5\times 7}$$

Multiply 5 and 7 to get 35.

$$y=\frac{59}{35}$$

The system is now solved.

$$x=\frac{7}{5} y=\frac{59}{35}$$