Chapter 9.8, Problem 12WE

To determine

To calculate: To find the real solutions

Answer to Problem 12WE

There are no solutions.

Explanation of Solution

Given information: System of equations $8x^2+y^2=25;8x^2-y^2=39$

Calculation:

Given the system of equations as follows:

  $\begin{array}{l}8x^2+y^2=25---(1)\\ 8x^2-y^2=39---(2)\end{array}$

Adding equations (1) and (2)

  $\begin{array}{l}16x^2=64\\ x^2=4\\ x=\pm 2\end{array}$

When $x=2$

  $\begin{array}{l}8{\left(2\right)}^2+y^2=25\\ y^2=25-32\\ y^2=-7\\ y=imaginarysolution\end{array}$

When $x=-2$

  $\begin{array}{l}8{\left(-2\right)}^2+y^2=25\\ y^2=25-32\\ y^2=-7\\ y=imaginarysolution\end{array}$

Conclusion:

Hence, there are no solutions.