Solve {l}{7x-11=22}{y=5x+8}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 7 x - 11 = 22 }\\ { y = 5 x + 8 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{221}{7} = 31\frac{4}{7} \approx 31.571428571$$

Solution Steps

Consider the first equation. Add 11 to both sides.

$$7x=22+11$$

Add 22 and 11 to get 33.

$$7x=33$$

Divide both sides by 7.

$$x=\frac{33}{7}$$

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

$$y=5\times \frac{33}{7}+8$$

Multiply 5 and \frac{33}{7} to get \frac{165}{7}.

$$y=\frac{165}{7}+8$$

Add \frac{165}{7} and 8 to get \frac{221}{7}.

$$y=\frac{221}{7}$$

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

$$z=\frac{221}{7}$$

The system is now solved.

$$x=\frac{33}{7} y=\frac{221}{7} z=\frac{221}{7}$$