Solve {l}{-5/2n=1000}{o=7n+2n^2}{p=o}{q=p}{r=q}{s=r}{t=s}{u=t}{v=u}{w=v}{x=w}{y=x}{z=y}{a=z}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { -\frac{5}{2} n = 1000 }\\ { o = 7 n + 2 n ^ {2} }\\ { p = o }\\ { q = p }\\ { r = q }\\ { s = r }\\ { t = s }\\ { u = t }\\ { v = u }\\ { w = v }\\ { x = w }\\ { y = x }\\ { z = y }\\ { a = z }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Solve for n, o, p, q, r, s, t, u, v, w, x, y, z, a, b, c

$$c=317200$$

Solution Steps

Consider the first equation. Multiply both sides by -\frac{2}{5}, the reciprocal of -\frac{5}{2}.

$$n=1000\left(-\frac{2}{5}\right)$$

Multiply 1000 and -\frac{2}{5} to get -400.

$$n=-400$$

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

$$o=7\left(-400\right)+2\left(-400\right)^{2}$$

Multiply 7 and -400 to get -2800.

$$o=-2800+2\left(-400\right)^{2}$$

Calculate -400 to the power of 2 and get 160000.

$$o=-2800+2\times 160000$$

Multiply 2 and 160000 to get 320000.

$$o=-2800+320000$$

Add -2800 and 320000 to get 317200.

$$o=317200$$

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

$$p=317200$$

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

$$q=317200$$

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

$$r=317200$$

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

$$s=317200$$

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

$$t=317200$$

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

$$u=317200$$

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

$$v=317200$$

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

$$w=317200$$

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

$$x=317200$$

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

$$y=317200$$

Consider the equation (13). Insert the known values of variables into the equation.

$$z=317200$$

Consider the equation (14). Insert the known values of variables into the equation.

$$a=317200$$

Consider the equation (15). Insert the known values of variables into the equation.

$$b=317200$$

Consider the equation (16). Insert the known values of variables into the equation.

$$c=317200$$

The system is now solved.

$$n=-400 o=317200 p=317200 q=317200 r=317200 s=317200 t=317200 u=317200 v=317200 w=317200 x=317200 y=317200 z=317200 a=317200 b=317200 c=317200$$