Solve {l}{x/{(1-3/2/5+4/5)}={(2/3*{(3-5/2)})}/{(3/frac{5}{4}-2)}}{y=15/{(1-frac{1}{5}/2)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x / {(1 - \frac{3}{2} / 5 + \frac{4}{5})} = {(\frac{2}{3} \cdot {(3 - \frac{5}{2})})} / {(3 / \frac{5}{4} - 2)} }\\ { y = 15 / {(1 - \frac{1}{5} / 2)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{50}{3} = 16\frac{2}{3} \approx 16.666666667$$

Solution Steps

Consider the first equation. Express \frac{\frac{3}{2}}{5} as a single fraction.

$$\frac{x}{1-\frac{3}{2\times 5}+\frac{4}{5}}=\frac{\frac{2}{3}\left(3-\frac{5}{2}\right)}{\frac{3}{\frac{5}{4}}-2}$$

Multiply 2 and 5 to get 10.

$$\frac{x}{1-\frac{3}{10}+\frac{4}{5}}=\frac{\frac{2}{3}\left(3-\frac{5}{2}\right)}{\frac{3}{\frac{5}{4}}-2}$$

Subtract \frac{3}{10} from 1 to get \frac{7}{10}.

$$\frac{x}{\frac{7}{10}+\frac{4}{5}}=\frac{\frac{2}{3}\left(3-\frac{5}{2}\right)}{\frac{3}{\frac{5}{4}}-2}$$

Add \frac{7}{10} and \frac{4}{5} to get \frac{3}{2}.

$$\frac{x}{\frac{3}{2}}=\frac{\frac{2}{3}\left(3-\frac{5}{2}\right)}{\frac{3}{\frac{5}{4}}-2}$$

Subtract \frac{5}{2} from 3 to get \frac{1}{2}.

$$\frac{x}{\frac{3}{2}}=\frac{\frac{2}{3}\times \frac{1}{2}}{\frac{3}{\frac{5}{4}}-2}$$

Multiply \frac{2}{3} and \frac{1}{2} to get \frac{1}{3}.

$$\frac{x}{\frac{3}{2}}=\frac{\frac{1}{3}}{\frac{3}{\frac{5}{4}}-2}$$

Divide 3 by \frac{5}{4} by multiplying 3 by the reciprocal of \frac{5}{4}.

$$\frac{x}{\frac{3}{2}}=\frac{\frac{1}{3}}{3\times \frac{4}{5}-2}$$

Multiply 3 and \frac{4}{5} to get \frac{12}{5}.

$$\frac{x}{\frac{3}{2}}=\frac{\frac{1}{3}}{\frac{12}{5}-2}$$

Subtract 2 from \frac{12}{5} to get \frac{2}{5}.

$$\frac{x}{\frac{3}{2}}=\frac{\frac{1}{3}}{\frac{2}{5}}$$

Divide \frac{1}{3} by \frac{2}{5} by multiplying \frac{1}{3} by the reciprocal of \frac{2}{5}.

$$\frac{x}{\frac{3}{2}}=\frac{1}{3}\times \frac{5}{2}$$

Multiply \frac{1}{3} and \frac{5}{2} to get \frac{5}{6}.

$$\frac{x}{\frac{3}{2}}=\frac{5}{6}$$

Multiply both sides by \frac{3}{2}.

$$x=\frac{5}{6}\times \frac{3}{2}$$

Multiply \frac{5}{6} and \frac{3}{2} to get \frac{5}{4}.

$$x=\frac{5}{4}$$

Consider the second equation. Express \frac{\frac{1}{5}}{2} as a single fraction.

$$y=\frac{15}{1-\frac{1}{5\times 2}}$$

Multiply 5 and 2 to get 10.

$$y=\frac{15}{1-\frac{1}{10}}$$

Subtract \frac{1}{10} from 1 to get \frac{9}{10}.

$$y=\frac{15}{\frac{9}{10}}$$

Divide 15 by \frac{9}{10} by multiplying 15 by the reciprocal of \frac{9}{10}.

$$y=15\times \frac{10}{9}$$

Multiply 15 and \frac{10}{9} to get \frac{50}{3}.

$$y=\frac{50}{3}$$

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

$$z=\frac{50}{3}$$

The system is now solved.

$$x=\frac{5}{4} y=\frac{50}{3} z=\frac{50}{3}$$