Chapter 9.7, Problem 7CYU

To determine

To find: The solution for the given system of the equation.

Answer to Problem 7CYU

The solution for the equation is $\left(\sqrt{17},-5\right),\left(-\sqrt{17},-5\right),\left(1,3\right),\left(-1,3\right)$ .

Explanation of Solution

Given:

The given system of equation is,

  $\begin{array}{l}{x}^2+2y=7\\ y^2-x^2=8\end{array}$

Calculation:

Consider the given equation are,

  $\begin{array}{l}{x}^2+2y=7\\ y^2-x^2=8\end{array}$

Add both the equation as,

  $\begin{array}{l}{x}^2+2y+y^2-x^2=7+8\\ 2y+y^2=15\\ \left(y+5\right)\left(y-3\right)=0\\ y=-5,3\end{array}$

Substitute $y=-5,3$ in the equation $x^2+2y=7$ as,

  $\begin{array}{l}{x}^2+2\left(-5\right)=7\\ x=\pm \sqrt{17}\end{array}$ and $\begin{array}{l}{x}^2+2\left(3\right)=7\\ x=\pm 1\end{array}$

Thus, the solution for the equation is $\left(\sqrt{17},-5\right),\left(-\sqrt{17},-5\right),\left(1,3\right),\left(-1,3\right)$ .