Solve {l}{x/5/7=0.8/11/7}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x / \frac{5}{7} = 0.8 / \frac{11}{7} }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=\frac{4}{11}\approx 0.363636364$$

Solution Steps

Consider the first equation. Divide 0.8 by \frac{11}{7} by multiplying 0.8 by the reciprocal of \frac{11}{7}.

$$\frac{x}{\frac{5}{7}}=0.8\times \frac{7}{11}$$

Multiply 0.8 and \frac{7}{11} to get \frac{28}{55}.

$$\frac{x}{\frac{5}{7}}=\frac{28}{55}$$

Multiply both sides by \frac{5}{7}.

$$x=\frac{28}{55}\times \frac{5}{7}$$

Multiply \frac{28}{55} and \frac{5}{7} to get \frac{4}{11}.

$$x=\frac{4}{11}$$

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

$$y=\frac{4}{11}$$

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

$$z=\frac{4}{11}$$

The system is now solved.

$$x=\frac{4}{11} y=\frac{4}{11} z=\frac{4}{11}$$