Solve {l}{9+15x-9x=sqrt{49/16}*{({(frac{2*{(5)}+3}{5})}-13/7)}}{y=0}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 9 + 15 x - 9 x = \sqrt{\frac{49}{16}} \cdot {({(\frac{2 \cdot {(5)} + 3}{5})} - \frac{13}{7})} }\\ { y = 0 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=0$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 35, the least common multiple of 5,7.

$$315+525x-315x=35\sqrt{\frac{49}{16}}\left(\frac{2\times 5+3}{5}-\frac{13}{7}\right)$$

Combine 525x and -315x to get 210x.

$$315+210x=35\sqrt{\frac{49}{16}}\left(\frac{2\times 5+3}{5}-\frac{13}{7}\right)$$

Rewrite the square root of the division \frac{49}{16} as the division of square roots \frac{\sqrt{49}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$315+210x=35\times \frac{7}{4}\left(\frac{2\times 5+3}{5}-\frac{13}{7}\right)$$

Multiply 35 and \frac{7}{4} to get \frac{245}{4}.

$$315+210x=\frac{245}{4}\left(\frac{2\times 5+3}{5}-\frac{13}{7}\right)$$

Multiply 2 and 5 to get 10.

$$315+210x=\frac{245}{4}\left(\frac{10+3}{5}-\frac{13}{7}\right)$$

Add 10 and 3 to get 13.

$$315+210x=\frac{245}{4}\left(\frac{13}{5}-\frac{13}{7}\right)$$

Subtract \frac{13}{7} from \frac{13}{5} to get \frac{26}{35}.

$$315+210x=\frac{245}{4}\times \frac{26}{35}$$

Multiply \frac{245}{4} and \frac{26}{35} to get \frac{91}{2}.

$$315+210x=\frac{91}{2}$$

Subtract 315 from both sides.

$$210x=\frac{91}{2}-315$$

Subtract 315 from \frac{91}{2} to get -\frac{539}{2}.

$$210x=-\frac{539}{2}$$

Divide both sides by 210.

$$x=\frac{-\frac{539}{2}}{210}$$

Express \frac{-\frac{539}{2}}{210} as a single fraction.

$$x=\frac{-539}{2\times 210}$$

Multiply 2 and 210 to get 420.

$$x=\frac{-539}{420}$$

Reduce the fraction \frac{-539}{420} to lowest terms by extracting and canceling out 7.

$$x=-\frac{77}{60}$$

The system is now solved.

$$x=-\frac{77}{60} y=0 z=0$$