How would you determine if lines intersected or not
if the lines were something like
y=-x-2
and
y=x^2+2-4
Well since you have two expressions involving x's and y's you can put them together.
$\displaystyle y=-x-2$ and $\displaystyle y=x^2+2x-4$ so $\displaystyle y=-x-2=x^2+2x-4$ by equating the y's.
So you need to solve $\displaystyle -x-2=x^2+2x-4$ to get the x co-ordinate. The y co-ordinate can then be found by substituting this x value into one of the two equations (they should give the same answer if you've done it right!).