Chapter 9.7, Problem 15WE

To determine

To estimate: the real solutions of the given system.

Answer to Problem 15WE

Therefore, the real solutions of the given system are $\left(-2,\text{ 0}\right),\left(2.5,\text{ 1}\right),$ , and $\left(2.5,-1\right)$ .

Explanation of Solution

Given:

  $\begin{array}{l}{x}^2-4y^2=4\\ 6y^2-x=2\end{array}$

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, note that the graphs intersect at three points $\left(-2,\text{ 0}\right),\left(2.5,\text{ 1}\right),$ and $\left(2.5,-1\right)$ .

Therefore, the real solutions of the given system are $\left(-2,\text{ 0}\right),\left(2.5,\text{ 1}\right),$ , and $\left(2.5,-1\right)$ .

Conclusion:

Therefore, the real solutions of the given system are $\left(-2,\text{ 0}\right),\left(2.5,\text{ 1}\right),$ , and $\left(2.5,-1\right)$ .