Chapter 9.8, Problem 15WE

To determine

To calculate: To find the real solutions

Answer to Problem 15WE

There are no real solution

Explanation of Solution

Given information: System of equations $5x^2+3y^2=7;3x^2-7y^2=13$

Calculation:

Given the system of equations as follows:

  $\begin{array}{l}5x^2+3y^2=7-----(1)\\ 3x^2-7y^2=13-----(2)\end{array}$

  $\begin{array}{l}5x^2+3y^2=7\times 7\\ 3x^2-7y^2=13\times 3\\ ---------------\\ 35x^2+21y^2=49----(3)\\ 9x^2-21y^2=39-----(4)\end{array}$

Adding equations (3) and (4)

  $\begin{array}{l}44x^2=88\\ x^2=2\\ x=\pm \sqrt{2}\end{array}$

When $x=\pm \sqrt{2}$

  $\begin{array}{l}5{\left(\pm 2\right)}^2+3y^2=7\\ 20+3y^2=7\\ 3y^2=-13\end{array}$

No real solution

Conclusion:

Hence, there are no real solutions