Q53. - Algebra 2

Question

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

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

Step-by-Step Solution

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 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 

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