Solve {l}{3/8y+2/5=1/2}{2*7x=4}{z=5x}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { \frac{3}{8} y + \frac{2}{5} = \frac{1}{2} }\\ { 2 \cdot 7 x = 4 }\\ { z = 5 x }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for y, x, z, a

$$a = \frac{10}{7} = 1\frac{3}{7} \approx 1.428571429$$

Solution Steps

Consider the first equation. Subtract \frac{2}{5} from both sides.

$$\frac{3}{8}y=\frac{1}{2}-\frac{2}{5}$$

Subtract \frac{2}{5} from \frac{1}{2} to get \frac{1}{10}.

$$\frac{3}{8}y=\frac{1}{10}$$

Multiply both sides by \frac{8}{3}, the reciprocal of \frac{3}{8}.

$$y=\frac{1}{10}\times \frac{8}{3}$$

Multiply \frac{1}{10} and \frac{8}{3} to get \frac{4}{15}.

$$y=\frac{4}{15}$$

Consider the second equation. Multiply 2 and 7 to get 14.

$$14x=4$$

Divide both sides by 14.

$$x=\frac{4}{14}$$

Reduce the fraction \frac{4}{14} to lowest terms by extracting and canceling out 2.

$$x=\frac{2}{7}$$

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

$$z=5\times \frac{2}{7}$$

Multiply 5 and \frac{2}{7} to get \frac{10}{7}.

$$z=\frac{10}{7}$$

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

$$a=\frac{10}{7}$$

The system is now solved.

$$y=\frac{4}{15} x=\frac{2}{7} z=\frac{10}{7} a=\frac{10}{7}$$