Solve {l}{6x-6y=23}{x=8}{z=y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 6 x - 6 y = 23 }\\ { x = 8 }\\ { z = y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z, a

$$a = \frac{25}{6} = 4\frac{1}{6} \approx 4.166666667$$

Solution Steps

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

$$6\times 8-6y=23$$

Multiply 6 and 8 to get 48.

$$48-6y=23$$

Subtract 48 from both sides.

$$-6y=23-48$$

Subtract 48 from 23 to get -25.

$$-6y=-25$$

Divide both sides by -6.

$$y=\frac{-25}{-6}$$

Fraction \frac{-25}{-6} can be simplified to \frac{25}{6} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{25}{6}$$

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

$$z=\frac{25}{6}$$

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

$$a=\frac{25}{6}$$

The system is now solved.

$$x=8 y=\frac{25}{6} z=\frac{25}{6} a=\frac{25}{6}$$