Solve {l}{81+{(-x)}=-{(frac{5*{(5)}+4}{5})}}{y=8}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 81 + {(-x)} = -{(\frac{5 \cdot {(5)} + 4}{5})} }\\ { y = 8 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=8$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 5.

$$405-5x=-\left(5\times 5+4\right)$$

Multiply 5 and 5 to get 25.

$$405-5x=-\left(25+4\right)$$

Add 25 and 4 to get 29.

$$405-5x=-29$$

Subtract 405 from both sides.

$$-5x=-29-405$$

Subtract 405 from -29 to get -434.

$$-5x=-434$$

Divide both sides by -5.

$$x=\frac{-434}{-5}$$

Fraction \frac{-434}{-5} can be simplified to \frac{434}{5} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{434}{5}$$

The system is now solved.

$$x=\frac{434}{5} y=8 z=8$$