Solve {l}{{(c)}1/3x+8=16}{1/3y=16-8}{1/3x=8}{z=x}{a=z}{b=a}{text{Solvefor}dtext{where}}{d=b}

$$\left. \begin{array} { l } { {(c)} \frac{1}{3} x + 8 = 16 }\\ { \frac{1}{3} y = 16 - 8 }\\ { \frac{1}{3} x = 8 }\\ { z = x }\\ { a = z }\\ { b = a }\\ { \text{Solve for } d \text{ where} } \\ { d = b } \end{array} \right.$$

Solve for c, x, y, z, a, b, d

$$d=24$$

Solution Steps

Consider the second equation. Subtract 8 from 16 to get 8.

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

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

$$y=8\times 3$$

Multiply 8 and 3 to get 24.

$$y=24$$

Consider the third equation. Multiply both sides by 3, the reciprocal of \frac{1}{3}.

$$x=8\times 3$$

Multiply 8 and 3 to get 24.

$$x=24$$

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

$$z=24$$

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

$$a=24$$

Consider the equation (6). Insert the known values of variables into the equation.

$$b=24$$

Consider the equation (7). Insert the known values of variables into the equation.

$$d=24$$

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

$$c\times \frac{1}{3}\times 24+8=16$$

Multiply \frac{1}{3} and 24 to get 8.

$$c\times 8+8=16$$

Subtract 8 from both sides.

$$c\times 8=16-8$$

Subtract 8 from 16 to get 8.

$$c\times 8=8$$

Divide both sides by 8.

$$c=\frac{8}{8}$$

Divide 8 by 8 to get 1.

$$c=1$$

The system is now solved.

$$c=1 x=24 y=24 z=24 a=24 b=24 d=24$$