Solve {l}{5x+4y=5}{6x+7x=6}

$$\left. \begin{array} { l } { 5 x + 4 y = 5 } \\ { 6 x + 7 x = 6 } \end{array} \right.$$

Solve for x, y

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

$$y=\frac{35}{52}\approx 0.673076923$$

Solution Steps

Consider the second equation. Combine 6x and 7x to get 13x.

$$13x=6$$

Divide both sides by 13.

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

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

$$5\times \frac{6}{13}+4y=5$$

Multiply 5 and \frac{6}{13} to get \frac{30}{13}.

$$\frac{30}{13}+4y=5$$

Subtract \frac{30}{13} from both sides.

$$4y=5-\frac{30}{13}$$

Subtract \frac{30}{13} from 5 to get \frac{35}{13}.

$$4y=\frac{35}{13}$$

Divide both sides by 4.

$$y=\frac{\frac{35}{13}}{4}$$

Express \frac{\frac{35}{13}}{4} as a single fraction.

$$y=\frac{35}{13\times 4}$$

Multiply 13 and 4 to get 52.

$$y=\frac{35}{52}$$

The system is now solved.

$$x=\frac{6}{13} y=\frac{35}{52}$$