Solve {l}{p=5/6}{q={(frac{7*{(2)}+1}{2})}-p}{r=q}{s=r}{t=s}{u=t}{v=u}{w=v}{x=w}{y=x}{z=y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { p = \frac{5}{6} }\\ { q = {(\frac{7 \cdot {(2)} + 1}{2})} - p }\\ { r = q }\\ { s = r }\\ { t = s }\\ { u = t }\\ { v = u }\\ { w = v }\\ { x = w }\\ { y = x }\\ { z = y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for p, q, r, s, t, u, v, w, x, y, z, a

$$a = \frac{20}{3} = 6\frac{2}{3} \approx 6.666666667$$

Solution Steps

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

$$q=\frac{7\times 2+1}{2}-\frac{5}{6}$$

Multiply 7 and 2 to get 14.

$$q=\frac{14+1}{2}-\frac{5}{6}$$

Add 14 and 1 to get 15.

$$q=\frac{15}{2}-\frac{5}{6}$$

Subtract \frac{5}{6} from \frac{15}{2} to get \frac{20}{3}.

$$q=\frac{20}{3}$$

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

$$r=\frac{20}{3}$$

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

$$s=\frac{20}{3}$$

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

$$t=\frac{20}{3}$$

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

$$u=\frac{20}{3}$$

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

$$v=\frac{20}{3}$$

Consider the equation (8). Insert the known values of variables into the equation.

$$w=\frac{20}{3}$$

Consider the equation (9). Insert the known values of variables into the equation.

$$x=\frac{20}{3}$$

Consider the equation (10). Insert the known values of variables into the equation.

$$y=\frac{20}{3}$$

Consider the equation (11). Insert the known values of variables into the equation.

$$z=\frac{20}{3}$$

Consider the equation (12). Insert the known values of variables into the equation.

$$a=\frac{20}{3}$$

The system is now solved.

$$p=\frac{5}{6} q=\frac{20}{3} r=\frac{20}{3} s=\frac{20}{3} t=\frac{20}{3} u=\frac{20}{3} v=\frac{20}{3} w=\frac{20}{3} x=\frac{20}{3} y=\frac{20}{3} z=\frac{20}{3} a=\frac{20}{3}$$