Solve {l}{1/2{(3x+6)}-25=0}{y=25{(4-2x)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{1}{2} {(3 x + 6)} - 25 = 0 }\\ { y = 25 {(4 - 2 x)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = -\frac{1900}{3} = -633\frac{1}{3} \approx -633.333333333$$

Solution Steps

Consider the first equation. Use the distributive property to multiply \frac{1}{2} by 3x+6.

$$\frac{3}{2}x+3-25=0$$

Subtract 25 from 3 to get -22.

$$\frac{3}{2}x-22=0$$

Add 22 to both sides. Anything plus zero gives itself.

$$\frac{3}{2}x=22$$

Multiply both sides by \frac{2}{3}, the reciprocal of \frac{3}{2}.

$$x=22\times \frac{2}{3}$$

Multiply 22 and \frac{2}{3} to get \frac{44}{3}.

$$x=\frac{44}{3}$$

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

$$y=25\left(4-2\times \frac{44}{3}\right)$$

Multiply -2 and \frac{44}{3} to get -\frac{88}{3}.

$$y=25\left(4-\frac{88}{3}\right)$$

Subtract \frac{88}{3} from 4 to get -\frac{76}{3}.

$$y=25\left(-\frac{76}{3}\right)$$

Multiply 25 and -\frac{76}{3} to get -\frac{1900}{3}.

$$y=-\frac{1900}{3}$$

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

$$z=-\frac{1900}{3}$$

The system is now solved.

$$x=\frac{44}{3} y=-\frac{1900}{3} z=-\frac{1900}{3}$$