Chapter 11.1, Problem 43SR

To determine

To find: The solutions of the given system of equations.

Answer to Problem 43SR

The solutions of the given system of equations are $x=\pm 8$ and $y=0$ .

Explanation of Solution

Given information:

The given equations are,

  $\begin{array}{l}{x}^2+y^2=64\\ x^2+64y^2=64\end{array}$

The given equation is,

  $x^2+64y^2=64$

Substitute $64-y^2$ for $x^2$ .

  $\begin{array}{l}\left(64-y^2\right)+64y^2=64\\ 63y^2=0\\ y=0\end{array}$

The value of $x$ is calculated as,

  $\begin{array}{l}{x}^2=64-y^2\\ x^2=64-0\\ x=\pm 8\end{array}$

Thus, the solutions of the given system of equations are $x=\pm 8$ and $y=3,-\frac{11}{4}$ .