Solve {l}{2-{({(x+1*5)}-5/8)}={(frac{2*{(125)}+7}{125})}}{y=4}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 2 - {({(x + 1 \cdot 5)} - \frac{5}{8})} = {(\frac{2 \cdot {(125)} + 7}{125})} }\\ { y = 4 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=4$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 1000, the least common multiple of 8,125.

$$2000-1000\left(x+1\times 5-\frac{5}{8}\right)=8\left(2\times 125+7\right)$$

Multiply 1 and 5 to get 5.

$$2000-1000\left(x+5-\frac{5}{8}\right)=8\left(2\times 125+7\right)$$

Subtract \frac{5}{8} from 5 to get \frac{35}{8}.

$$2000-1000\left(x+\frac{35}{8}\right)=8\left(2\times 125+7\right)$$

Use the distributive property to multiply -1000 by x+\frac{35}{8}.

$$2000-1000x-4375=8\left(2\times 125+7\right)$$

Subtract 4375 from 2000 to get -2375.

$$-2375-1000x=8\left(2\times 125+7\right)$$

Multiply 2 and 125 to get 250.

$$-2375-1000x=8\left(250+7\right)$$

Add 250 and 7 to get 257.

$$-2375-1000x=8\times 257$$

Multiply 8 and 257 to get 2056.

$$-2375-1000x=2056$$

Add 2375 to both sides.

$$-1000x=2056+2375$$

Add 2056 and 2375 to get 4431.

$$-1000x=4431$$

Divide both sides by -1000.

$$x=-\frac{4431}{1000}$$

The system is now solved.

$$x=-\frac{4431}{1000} y=4 z=4$$