Solve {l}{7.5{(x+8.3)}=-4.5{(x+8.9)}+199.5}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 7.5 {(x + 8.3)} = -4.5 {(x + 8.9)} + 199.5 }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=8.1$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 7.5 by x+8.3.

$$7.5x+62.25=-4.5\left(x+8.9\right)+199.5$$

Use the distributive property to multiply -4.5 by x+8.9.

$$7.5x+62.25=-4.5x-40.05+199.5$$

Add -40.05 and 199.5 to get 159.45.

$$7.5x+62.25=-4.5x+159.45$$

Add 4.5x to both sides.

$$7.5x+62.25+4.5x=159.45$$

Combine 7.5x and 4.5x to get 12x.

$$12x+62.25=159.45$$

Subtract 62.25 from both sides.

$$12x=159.45-62.25$$

Subtract 62.25 from 159.45 to get 97.2.

$$12x=97.2$$

Divide both sides by 12.

$$x=\frac{97.2}{12}$$

Expand \frac{97.2}{12} by multiplying both numerator and the denominator by 10.

$$x=\frac{972}{120}$$

Reduce the fraction \frac{972}{120} to lowest terms by extracting and canceling out 12.

$$x=\frac{81}{10}$$

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

$$y=\frac{81}{10}$$

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

$$z=\frac{81}{10}$$

The system is now solved.

$$x=\frac{81}{10} y=\frac{81}{10} z=\frac{81}{10}$$