Q. 25 - Precalculus Enhanced with Graphing Utilities

Question

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

$\left\{\begin{array}{l}2x^2+ y^2 =18 \\ xy=4\end{array}\right.$

Step-by-Step Solution

Answer

the point of intersection is $(2\sqrt{2},\sqrt{2}),(-2\sqrt{2},-\sqrt{2}),(1,4),(-1,-4)$.

Step 1. Given

$\left\{\begin{array}{l}2x^2+ y^2 =18 \\ xy=4\end{array}\right.$

Step 2. Graphing each equation

$2x^2+ y^2 =18$

$xy=4$

Step 3. Calculation of intersection point

$$\begin{gathered} Consider, \\ {y}^2+2 x^2 =18 .....\left(1\right) \\ xy=4 .....\left(2\right) \\ x=\frac{4}{y} \& \\ y=\pm \sqrt{18-2x^2} \end{gathered}$$

$x$	$y=\frac{4}{x}$	$y=\pm \sqrt{18-2x^2}$
1	4	4
2	2	$\sqrt{10}$
$2\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$
-1	-4	$-4$
-2$\sqrt{2}$	$-\sqrt{2}$	$-\sqrt{2}$