Sample answer to Question B on the class activity "Transforming Words to Equations - Part 1"


(1) The definition of the graph of an equation is, "All points whose coordinates satisfy the equation."

(2) A point lies on the intersection of two graphs of equations if and only if it lies on each graph. (This is by the definition of intersection.)

Applying the definition of graph (1), we transform (2)  to:

(3) A point lies on the intersection of two graphs of equations if and only if its coordinates satisfy each equation.

This gives us a practical means of finding the points of intersection: Solve the two equations simultaneously (that is, find pairs that satisfy both equations) to find the coordinates of the points of intersection.