Quandaries and Queries


1. How do you interpret the solution of a system of equations by the corresponding graph? Demonstrate your answer by the use of an example.
2. What is the situation when two linear inequalities have no solution?


Hi Gina,

Lets look at the equation

x + y = 7

Its graph is the collection of points in the plane whose x and y coordinated have a sum of 7. Thus (3,4) is on the graph since 3 + 4 = 7, and (3,6) is not on the graph since 3 + 6 is not 7. We say that a point "satisfies" the equation if, after substituting the coordinates of the point into the equation, the equation becomes a numerically true fact. ( 3,4) satisfies the equation since

3 + 4 = 7 is true

and (3,6) does not satisfy the equation seine

3 + 6 = 7 is not true.

If a point in the plane satisfies the equation then it is on the graph of the equation, and if a point in the plane is on the graph of the equation then it satisfies the equation.

Suppose now you add a second equation

x - 2y = 1

A solution to this system of two equations is a point that satisfies both equations, and hence must lie on both graphs. Likewise a point that lies on both graphs satisfies both equations.

Now try it. plot the graphs of both equations reasonably accurately and see what points lie on both graphs. Now solve this system of two equations and compare.