Solve {l}{2+3x/10-7-3x/5=0}{y=8*{(1-1/8+1/8x)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{2 + 3 x}{10} - \frac{7 - 3 x}{5} = 0 }\\ { y = 8 \cdot {(1 - \frac{1}{8} + \frac{1}{8} x)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{25}{3} = 8\frac{1}{3} \approx 8.333333333$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 10, the least common multiple of 10,5.

$$2+3x-2\left(7-3x\right)=0$$

Use the distributive property to multiply -2 by 7-3x.

$$2+3x-14+6x=0$$

Subtract 14 from 2 to get -12.

$$-12+3x+6x=0$$

Combine 3x and 6x to get 9x.

$$-12+9x=0$$

Add 12 to both sides. Anything plus zero gives itself.

$$9x=12$$

Divide both sides by 9.

$$x=\frac{12}{9}$$

Reduce the fraction \frac{12}{9} to lowest terms by extracting and canceling out 3.

$$x=\frac{4}{3}$$

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

$$y=8\left(1-\frac{1}{8}+\frac{1}{8}\times \frac{4}{3}\right)$$

Subtract \frac{1}{8} from 1 to get \frac{7}{8}.

$$y=8\left(\frac{7}{8}+\frac{1}{8}\times \frac{4}{3}\right)$$

Multiply \frac{1}{8} and \frac{4}{3} to get \frac{1}{6}.

$$y=8\left(\frac{7}{8}+\frac{1}{6}\right)$$

Add \frac{7}{8} and \frac{1}{6} to get \frac{25}{24}.

$$y=8\times \frac{25}{24}$$

Multiply 8 and \frac{25}{24} to get \frac{25}{3}.

$$y=\frac{25}{3}$$

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

$$z=\frac{25}{3}$$

The system is now solved.

$$x=\frac{4}{3} y=\frac{25}{3} z=\frac{25}{3}$$