Question

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

$\left\{\begin{array}{l}y=2x+1\\ 2x^2+y^2=1\end{array}\right.$

Short answer

The point of intersection is $(0,1)\&\left(-\frac{2}{3},\frac{1}{3}\right)$.

Step-by-step solution

Step 1. Given information

$\left\{\begin{array}{l}y=2x+1\\ 2x^2+y^2=1\end{array}\right.$

Step 2. Graphing each equation

$y=2x+1$

$2x^2+y^2=1$

Step 3. Calculation of intersection point

$$\begin{gathered} Consider, \\ y=2x+1.....\left(1\right) \\ 2x^2+y^2=1.....\left(2\right) \\ Nowsubstitutingthevalueofyfromeq.1intoeq.2 \\ weget \\ 2x^2+{(2x+1)}^2=12x^2+4x^2+4x+1=1 \\ 6x^2+4x=0 \\ x=0,-\frac{2}{3} \\ Nowsubstitutingvalueofxineq.1weget \\ y=2\left(0\right)+1 \\ y=1 \\ y=2\left(-\frac{2}{3}\right)+1 \\ y=-\frac{1}{3} \end{gathered}$$