Chapter 9.7, Problem 13WE

To determine

To estimate: the real solutions of the given system.

Answer to Problem 13WE

The four real solutions of the given system are $\left(-4.5,-2\right),\left(2,4.5\right),\left(4.5,2\right)$ , and $\left(-2,-4.5\right)$ .

Explanation of Solution

Given:

  $\begin{array}{l}{x}^2+y^2=25\\ xy=10\end{array}$

Calculation:

The real solutions of such a system can be determined by finding the points at which the individual quadratic graphs intersect.

Let us graph the two given equations on the same co-ordinate plane, and find the number of points at which they intersect.

  

From the graph, it can be seen that the graphs intersect at four points $\left(-4.5,-2\right),\left(2,4.5\right),\left(4.5,2\right)$ , and $\left(-2,-4.5\right)$ .

Therefore, the four real solutions of the given system are $\left(-4.5,-2\right),\left(2,4.5\right),\left(4.5,2\right)$ , and $\left(-2,-4.5\right)$ .

Conclusion:

Therefore, the four real solutions of the given system are $\left(-4.5,-2\right),\left(2,4.5\right),\left(4.5,2\right)$ , and $\left(-2,-4.5\right)$ .