Please a lot of points involved.

To find points of intersection, we need to use simultaneous equations.

y = 2x   --- 1
y = [tex] x^{2} [/tex] - 3   --- 2

Sub 1 into 2,

2x = [tex] x^{2} [/tex] - 3
0 = [tex] x^{2} [/tex] - 2x - 3
[tex] x^{2} [/tex] - 2x - 3 = 0

Factorise,

(x - 3)(x + 1) = 0

Let each bracket equal to 0,

x - 3 = 0               x + 1 = 0
     x = 3                     x = -1

Sub 3 into equation 1,

y = 2(3)
   = 6

Now sub -1 into equation 1,

y = 2(-1)
   = -2

Therefore, your two y values are -2 and 6

Hope this helped! Ask me if there's any part of the working you don't understand :)