Solve {l}{8{(42*2y)}=16}{z={(21-y)}}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 8 {(42 \cdot 2 y)} = 16 }\\ { z = {(21 - y)} }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for y, z, a

$$a = \frac{881}{42} = 20\frac{41}{42} \approx 20.976190476$$

Solution Steps

Consider the first equation. Multiply 8 and 42 to get 336.

$$336\times 2y=16$$

Multiply 336 and 2 to get 672.

$$672y=16$$

Divide both sides by 672.

$$y=\frac{16}{672}$$

Reduce the fraction \frac{16}{672} to lowest terms by extracting and canceling out 16.

$$y=\frac{1}{42}$$

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

$$z=21-\frac{1}{42}$$

Subtract \frac{1}{42} from 21 to get \frac{881}{42}.

$$z=\frac{881}{42}$$

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

$$a=\frac{881}{42}$$

The system is now solved.

$$y=\frac{1}{42} z=\frac{881}{42} a=\frac{881}{42}$$