“Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination.”
Graphing systems of equations involves incorporating many skills we have previously studied: operations with integers (here and here you can find computational problems involving integers and answers); solving equations; graphing linear equations; and understanding the advantages of the three different forms of equations. The question that we will work toward in this chapter follows these two paragraphs: Suppose that in January of 2008 the Sheldon Forest contained 8,000 trees. Unfortunately trees are dying at a constant rate of Anthracnose, a disease affecting maples. In November of 2008, the Sheldon Forest had 7,600 trees and in November of 2009, the Sheldon Forest had 7,120 trees. The Highgate Forest has seen a constant growth in the number of trees. In January 2008, there were 5,000 trees in the forest. In November of 2008 researchers counted 5,300 trees and in November 2009 there were 5,600 trees.
When (if ever) will the two forests have the same number of trees? In the next few weeks, we will learn multiple ways to tackle this and similar problems. |  Above is one means of solving systems of linear equations. Notice the solution is the ordered pair (3, 0) where the two lines intersect or meet. |