Solve {l}{5x=7y}{3y=5z}{1z=5}

$$\left. \begin{array} { l } { 5 x = 7 y } \\ { 3 y = 5 z } \\ { 1 z = 5 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{35}{3} = 11\frac{2}{3} \approx 11.666666667$$

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

$$z=5$$

Solution Steps

Consider the third equation. Divide both sides by 1.

$$z=5$$

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

$$3y=5\times 5$$

Multiply 5 and 5 to get 25.

$$3y=25$$

Divide both sides by 3.

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

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

$$5x=7\times \frac{25}{3}$$

Multiply 7 and \frac{25}{3} to get \frac{175}{3}.

$$5x=\frac{175}{3}$$

Divide both sides by 5.

$$x=\frac{\frac{175}{3}}{5}$$

Express \frac{\frac{175}{3}}{5} as a single fraction.

$$x=\frac{175}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$x=\frac{175}{15}$$

Reduce the fraction \frac{175}{15} to lowest terms by extracting and canceling out 5.

$$x=\frac{35}{3}$$

The system is now solved.

$$x=\frac{35}{3} y=\frac{25}{3} z=5$$