When 2 lines intersect means when there equations are equal. So so we can take both equations and set them equal like so:
y= 2x
y= x^2 - 3
I can do y=y or the one I need is:
x^2 - 3 = 2x
So move them to one side and it becomes:
x^2 - 2x - 3 = 0
factor these and get
(x - 3) * (x + 1) = 0
When equation is like this you have to remember that anything multiplied by 0 will equal 0. So for this to be be possible, one of the values in either parenthesis must be come out to 0 like this:
(x - 3 = 0) * (x + 1) = 0
Or
(x - 3) * (x + 1 =0) = 0
so that means we can evaluate the equations in either parenthesis and either answer is possible. So:
x - 3 = 0
x = 3
and:
x + 1 = 0
x = -1
But but it did not ask for x values. it asked for t values. So plug in x values and get
2 * 3 = y
y = 6
And:
2 * -1 = y
y = -2
that will be the answers. You can check by plugging into other equation using the coordinate values:
(3,6) and (-1,-2)
so:
y= x^2 - 3
6 = 3^2 - 3
6 = 6
And
y= x^2 - 3
-2 = 1^2 - 3
-2 = -2
since both answers balance out, they values we found are correct. good luck
