Solve {l}{4x+2f=130}{17+5f=55}

$$\left. \begin{array} { l } { 4 x + 2 f = 130 } \\ { 17 + 5 f = 55 } \end{array} \right.$$

Solve for x, f

$$x = \frac{287}{10} = 28\frac{7}{10} = 28.7$$

$$f = \frac{38}{5} = 7\frac{3}{5} = 7.6$$

Solution Steps

Consider the second equation. Subtract 17 from both sides.

$$5f=55-17$$

Subtract 17 from 55 to get 38.

$$5f=38$$

Divide both sides by 5.

$$f=\frac{38}{5}$$

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

$$4x+2\times \frac{38}{5}=130$$

Multiply 2 and \frac{38}{5} to get \frac{76}{5}.

$$4x+\frac{76}{5}=130$$

Subtract \frac{76}{5} from both sides.

$$4x=130-\frac{76}{5}$$

Subtract \frac{76}{5} from 130 to get \frac{574}{5}.

$$4x=\frac{574}{5}$$

Divide both sides by 4.

$$x=\frac{\frac{574}{5}}{4}$$

Express \frac{\frac{574}{5}}{4} as a single fraction.

$$x=\frac{574}{5\times 4}$$

Multiply 5 and 4 to get 20.

$$x=\frac{574}{20}$$

Reduce the fraction \frac{574}{20} to lowest terms by extracting and canceling out 2.

$$x=\frac{287}{10}$$

The system is now solved.

$$x=\frac{287}{10} f=\frac{38}{5}$$