Chapter 9.8, Problem 11WE

To determine

To calculate: To find the real solutions

Answer to Problem 11WE

Solutions are $\left(4,3\right),\left(4,-3\right),\left(-4,3\right),\left(-4,-3\right)$

Explanation of Solution

Given information: System of equations $x^2+y^2=25;x^2-y^2=7$

Calculation:

Given the system of equations as follows:

  $\begin{array}{l}{x}^2+y^2=25--(1)\\ x^2-y^2=7--(2)\end{array}$

Adding equations (1) and (2)

  $\begin{array}{l}2x^2=32\\ x^2=16\\ x=\pm 4\end{array}$

When $x=4$

  $\begin{array}{l}{\left(4\right)}^2+y^2=25\\ y^2=25-16\\ y^2=9\\ y=\pm 3\end{array}$

When $x=-4$

  $\begin{array}{l}{\left(-4\right)}^2+y^2=25\\ y^2=25-16\\ y^2=9\\ y=\pm 3\end{array}$

Conclusion:

Hence, solutions are $\left(4,3\right),\left(4,-3\right),\left(-4,3\right),\left(-4,-3\right)$