Q. 37 - Precalculus Enhanced with Graphing Utilities

Question

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

$$\begin{gathered} x^2+2xy=10 \\ 3x^2-xy=2 \end{gathered}$$

Step-by-Step Solution

Answer

The point of intersection is  $\left(\sqrt{2},2\sqrt{2}\right),\left(-\sqrt{2},-2\sqrt{2}\right)$.

Step 1. Given information

$$\begin{gathered} x^2+2xy=10 \\ 3x^2-xy=2 \end{gathered}$$

Step 2. Graphing each equation

$x^2+2xy=10$

$3x^2-xy=2$

Step 3. Calculation of intersection point

$$\begin{gathered} Consider, \\ {x}^2+2xy=10 ......\left(1\right) \\ 3x^2-xy=2 .......\left(2\right) \\ Multiply 2 with eq. 2 and add with eq.1 \\ we get \\ 7x^2=14 \\ x=\pm \sqrt{2} \\ substitute x=\pm \sqrt{2} in eq. 2 to get y \\ x=\sqrt{2} \\ y=2\sqrt{2} \\ x=-\sqrt{2} \\ y=-2\sqrt{2} \end{gathered}$$