Analyze the solutions of systems of equations graphically

Analyze the solutions of systems of equations graphically
Description
Exercise Name:	Analyze the solutions of systems of equations graphically
Math Missions:	8th grade (U.S.) Math Mission, Algebra I Math Mission, Mathematics II Math Mission, Algebra II Math Mission, Mathematics III Math Mission
Types of Problems:	2

The Analyze the solutions of systems of equations graphically exercise appears under the 8th grade (U.S.) Math Mission, Algebra I Math Mission, Mathematics II Math Mission, Algebra II Math Mission and Mathematics III 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 user selects how many solutions there are to the pictured system.

   

   Tell how many solutions the graph has

2. Make a line with a certain number of solutions: This problem has a coordinate plane with one line already drawn. The user is asked to draw a second line to illustrate a particular type of system subject to a collection of constraints.

   

   Make a line with a certain number of solutions

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.
5. Knowledge of algebra is essential for higher math levels like trigonometry and calculus. Algebra also has countless applications in the real world.