|Analyze the solutions of systems of equations graphically|
|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:
- 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.
- 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.
Graphing skills are helpful but not necessary as the rules can be memorized from the pictures to solve this exercise.
- Lines that cross each other have a single solution.
- Lines that are coincident (completely overlap) have infinitely many solutions.
- Lines that are parallel have no solutions.
- 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.
- Systems of equations are used to solve some mixture problems in chemistry.
- Systems of equations are used to solve distance, rate, time problems in physics.
- Systems of equations can be used with certain Cost and Revenue situations to find break-even points.
- Systems of equations can be used with supply and demand to find equilibrium prices.
- Knowledge of algebra is essential for higher math levels like trigonometry and calculus. Algebra also has countless applications in the real world.