Analyze the solutions of systems of equations graphically

The  exercise appears under the 8th Grade Math Mission. This exercise strengthens the relationship between the graph of a system of equations and how many solutions the system has.

Types of Problems
There are two types of problems in this exercise:


 * 1) Tell how many solutions the graph has: This problem presents two lines drawn on a coordinate plane. The student selects how many solutions there are to the pictured system.Gswozois1.png
 * 2) Make a line with a certain number of solutions: This problem has a coordinate plane with one line already drawn. The student is asked to draw a second line to illustrate a particular type of system subject to a collection of constraints.Gswozois2.png

Strategies
Graphing skills are helpful but not necessary as the rules can be memorized from the pictures to solve this exercise.
 * 1) Lines that cross each other have a single solution.
 * 2) Lines that are coincident (completely overlap) have infinitely many solutions.
 * 3) Lines that are parallel have no solutions.
 * 4) To graph lines on Make a line with a certain number of solutions it is not necessary to use difficult points. There should be integral coordinates that will work to make the line.

Real-life applications

 * 1) Systems of equations are used to solve some mixture problems in chemistry.
 * 2) Systems of equations are used to solve distance, rate, time problems in physics.
 * 3) Systems of equations can be used with certain Cost and Revenue situations to find break-even points.
 * 4) Systems of equations can be used with supply and demand to find equilibrium prices.