Solve {l}{-5/2n=1000}{o=7n+2n^2}{p=o}{q=p}{text{Solvefor}rtext{where}}{r=q}

$$\left. \begin{array} { l } { -\frac{5}{2} n = 1000 }\\ { o = 7 n + 2 n ^ {2} }\\ { p = o }\\ { q = p }\\ { \text{Solve for } r \text{ where} } \\ { r = q } \end{array} \right.$$

Solve for n, o, p, q, r

$$r=317200$$

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.

$$r=317200$$

The system is now solved.

$$n=-400 o=317200 p=317200 q=317200 r=317200$$