Quadratics, Intersecting Parabola and Line, How to Find the the Points of Intersection by Hand.

Given a parabola and a line, we learn how to find the coordinates of their points of intersection without a calculator, by hand.
The method is used is sometimes called "equating the y's" and is summarised in 3 steps:
Step 1 : we equate the two expression we have for y and rearrange to form a solvable quadratic equation
Step 2: we solve the quadratic equation, which leads to the x coordinates of the points of intersection
Step 3: we find the y coordinates of the points of intersection using the line equation