Question

Find the exact solution(s) of each system of equations.

$\begin{array}{l}{x}^2+2y^2=33\\ x^2-y^2=9\end{array}$

Short answer

The solutions to the system of equations is

$\left(-4.1,2.8\right),\left(-4.1,-2.8\right),\left(4.1,2.8\right),\left(4.1,-2.8\right)$

Step-by-step solution

Step 1. Given Information.

Given to find the exact solutions of the system of equations:

$\begin{array}{l}{x}^2+2y^2=33\\ x^2-y^2=9\end{array}$

Step 2. Explanation.

Solving the system of equations using graphic calculator:

From the graph, the two graphs intersect at the points

$\left(-4.1,2.8\right),\left(-4.1,-2.8\right),\left(4.1,2.8\right),\left(4.1,-2.8\right)$

Step 3. Conclusion.

Hence, the solutions to the system of equations is

$\left(-4.1,2.8\right),\left(-4.1,-2.8\right),\left(4.1,2.8\right),\left(4.1,-2.8\right)$