Solve {r}{7x-8y=6}{4x-24=-3}

$$\left. \begin{array} { r } { 7 x - 8 y = 6 } \\ { 4 x - 24 = - 3 } \end{array} \right.$$

Solve for x, y

$$x = \frac{21}{4} = 5\frac{1}{4} = 5.25$$

$$y = \frac{123}{32} = 3\frac{27}{32} = 3.84375$$

Solution Steps

Consider the second equation. Add 24 to both sides.

$$4x=-3+24$$

Add -3 and 24 to get 21.

$$4x=21$$

Divide both sides by 4.

$$x=\frac{21}{4}$$

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

$$7\times \frac{21}{4}-8y=6$$

Multiply 7 and \frac{21}{4} to get \frac{147}{4}.

$$\frac{147}{4}-8y=6$$

Subtract \frac{147}{4} from both sides.

$$-8y=6-\frac{147}{4}$$

Subtract \frac{147}{4} from 6 to get -\frac{123}{4}.

$$-8y=-\frac{123}{4}$$

Divide both sides by -8.

$$y=\frac{-\frac{123}{4}}{-8}$$

Express \frac{-\frac{123}{4}}{-8} as a single fraction.

$$y=\frac{-123}{4\left(-8\right)}$$

Multiply 4 and -8 to get -32.

$$y=\frac{-123}{-32}$$

Fraction \frac{-123}{-32} can be simplified to \frac{123}{32} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{123}{32}$$

The system is now solved.

$$x=\frac{21}{4} y=\frac{123}{32}$$