Solve {l}{5+13x-7x=sqrt{25}*{(33/6-5/4)}}{y=2}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 5 + 13 x - 7 x = \sqrt{25} \cdot {(\frac{33}{6} - \frac{5}{4})} }\\ { y = 2 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=2$$

Solution Steps

Consider the first equation. Combine 13x and -7x to get 6x.

$$5+6x=\sqrt{25}\left(\frac{33}{6}-\frac{5}{4}\right)$$

Calculate the square root of 25 and get 5.

$$5+6x=5\left(\frac{33}{6}-\frac{5}{4}\right)$$

Reduce the fraction \frac{33}{6} to lowest terms by extracting and canceling out 3.

$$5+6x=5\left(\frac{11}{2}-\frac{5}{4}\right)$$

Subtract \frac{5}{4} from \frac{11}{2} to get \frac{17}{4}.

$$5+6x=5\times \frac{17}{4}$$

Multiply 5 and \frac{17}{4} to get \frac{85}{4}.

$$5+6x=\frac{85}{4}$$

Subtract 5 from both sides.

$$6x=\frac{85}{4}-5$$

Subtract 5 from \frac{85}{4} to get \frac{65}{4}.

$$6x=\frac{65}{4}$$

Divide both sides by 6.

$$x=\frac{\frac{65}{4}}{6}$$

Express \frac{\frac{65}{4}}{6} as a single fraction.

$$x=\frac{65}{4\times 6}$$

Multiply 4 and 6 to get 24.

$$x=\frac{65}{24}$$

The system is now solved.

$$x=\frac{65}{24} y=2 z=2$$