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.