Q. 24 - Precalculus Enhanced with Graphing Utilities

Question

graph each equation of the system. Then solve the system to find the points of intersection.

$\left\{\begin{array}{l}y{ }^2+x^2=10 \\ xy=3\end{array}\right.$

Step-by-Step Solution

Answer

the point of intersection is $(3,1),(1,3),(-1,-3) and (-3,-1)$..

Step 1. Given

$\left\{\begin{array}{l}y{ }^2+x^2=10 \\ xy=3\end{array}\right.$

Step 2. Graphing each equation

$y{ }^2+x^2=10$

$xy=3$

Step 3. Calculation of intersection point

$$\begin{gathered} Consider, \\ {y}^2+ x^2 =10 .....\left(1\right) \\ xy=3 .....\left(2\right) \\ Now substituting the value of y from eq.2 into eq.1 \\ we get \\ y=\frac{3}{x} \& y=\pm \sqrt{10-x^2} \end{gathered}$$