Solve {l}{7*-2y=26}{5x+4y=24}

$$\left. \begin{array} { l } { 7 \times - 2 y = 26 } \\ { 5 x + 4 y = 24 } \end{array} \right.$$

Solve for y, x

$$x = \frac{44}{7} = 6\frac{2}{7} \approx 6.285714286$$

$$y = -\frac{13}{7} = -1\frac{6}{7} \approx -1.857142857$$

Solution Steps

Consider the first equation. Multiply 7 and -2 to get -14.

$$-14y=26$$

Divide both sides by -14.

$$y=\frac{26}{-14}$$

Reduce the fraction \frac{26}{-14} to lowest terms by extracting and canceling out 2.

$$y=-\frac{13}{7}$$

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

$$5x+4\left(-\frac{13}{7}\right)=24$$

Multiply 4 and -\frac{13}{7} to get -\frac{52}{7}.

$$5x-\frac{52}{7}=24$$

Add \frac{52}{7} to both sides.

$$5x=24+\frac{52}{7}$$

Add 24 and \frac{52}{7} to get \frac{220}{7}.

$$5x=\frac{220}{7}$$

Divide both sides by 5.

$$x=\frac{\frac{220}{7}}{5}$$

Express \frac{\frac{220}{7}}{5} as a single fraction.

$$x=\frac{220}{7\times 5}$$

Multiply 7 and 5 to get 35.

$$x=\frac{220}{35}$$

Reduce the fraction \frac{220}{35} to lowest terms by extracting and canceling out 5.

$$x=\frac{44}{7}$$

The system is now solved.

$$y=-\frac{13}{7} x=\frac{44}{7}$$