Solve {l}{5x+x-7=3}{y=31-x+x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 5 x + x - 7 = 3 }\\ { y = 31 - x + x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=31$$

Solution Steps

Consider the first equation. Combine 5x and x to get 6x.

$$6x-7=3$$

Add 7 to both sides.

$$6x=3+7$$

Add 3 and 7 to get 10.

$$6x=10$$

Divide both sides by 6.

$$x=\frac{10}{6}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{5}{3}$$

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

$$y=31-\frac{5}{3}+\frac{5}{3}$$

Subtract \frac{5}{3} from 31 to get \frac{88}{3}.

$$y=\frac{88}{3}+\frac{5}{3}$$

Add \frac{88}{3} and \frac{5}{3} to get 31.

$$y=31$$

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

$$z=31$$

The system is now solved.

$$x=\frac{5}{3} y=31 z=31$$