Find the intersection point of the line 2y=x+3 with the ellipse y^2+2x^2=3

The first step is to rearrange for x: we have x=2y-3now we can plug this into the equation of the ellipse: y^2+2(2y-3)^2=39y^2-24y+15 = 0we can use the quadratic formula to solve this equation:y = (24+-sqrt(24^2-4915))/2*9y = (24+-6)/18y= 5/3, 1Next we need to find the corresponding values of x which can be done by plugging the values of y into the expression we found for xat y=5/3 we have x = 1/3at y = 1 we have x = -1so the points of intersection are (1/3,5/3) and (-1,1)