Solve {l}{4*26y=48}{3x+2y=51}

$$\left. \begin{array} { l } { 4 \times 26 y = 48 } \\ { 3 x + 2 y = 51 } \end{array} \right.$$

Solve for y, x

$$x = \frac{217}{13} = 16\frac{9}{13} \approx 16.692307692$$

$$y=\frac{6}{13}\approx 0.461538462$$

Solution Steps

Consider the first equation. Multiply 4 and 26 to get 104.

$$104y=48$$

Divide both sides by 104.

$$y=\frac{48}{104}$$

Reduce the fraction \frac{48}{104} to lowest terms by extracting and canceling out 8.

$$y=\frac{6}{13}$$

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

$$3x+2\times \frac{6}{13}=51$$

Multiply 2 and \frac{6}{13} to get \frac{12}{13}.

$$3x+\frac{12}{13}=51$$

Subtract \frac{12}{13} from both sides.

$$3x=51-\frac{12}{13}$$

Subtract \frac{12}{13} from 51 to get \frac{651}{13}.

$$3x=\frac{651}{13}$$

Divide both sides by 3.

$$x=\frac{\frac{651}{13}}{3}$$

Express \frac{\frac{651}{13}}{3} as a single fraction.

$$x=\frac{651}{13\times 3}$$

Multiply 13 and 3 to get 39.

$$x=\frac{651}{39}$$

Reduce the fraction \frac{651}{39} to lowest terms by extracting and canceling out 3.

$$x=\frac{217}{13}$$

The system is now solved.

$$y=\frac{6}{13} x=\frac{217}{13}$$