Solve {l}{34+5n=42}{3n+5y=98}

$$\left. \begin{array} { l } { 34 + 5 n = 42 } \\ { 3 n + 5 y = 98 } \end{array} \right.$$

Solve for n, y

$$y = \frac{466}{25} = 18\frac{16}{25} = 18.64$$

$$n = \frac{8}{5} = 1\frac{3}{5} = 1.6$$

Solution Steps

Consider the first equation. Subtract 34 from both sides.

$$5n=42-34$$

Subtract 34 from 42 to get 8.

$$5n=8$$

Divide both sides by 5.

$$n=\frac{8}{5}$$

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

$$3\times \frac{8}{5}+5y=98$$

Multiply 3 and \frac{8}{5} to get \frac{24}{5}.

$$\frac{24}{5}+5y=98$$

Subtract \frac{24}{5} from both sides.

$$5y=98-\frac{24}{5}$$

Subtract \frac{24}{5} from 98 to get \frac{466}{5}.

$$5y=\frac{466}{5}$$

Divide both sides by 5.

$$y=\frac{\frac{466}{5}}{5}$$

Express \frac{\frac{466}{5}}{5} as a single fraction.

$$y=\frac{466}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$y=\frac{466}{25}$$

The system is now solved.

$$n=\frac{8}{5} y=\frac{466}{25}$$