Graphically understanding solution methods to systems of equations

The  exercise appears under the Algebra I Math Mission. This exercise attempts to explore the relationship between arithmetic operations on equations and the results when compared with original systems

Types of Problems
There is one type of problem in this exercise:


 * 1) Satisfy the multiple requests: This problem has a system of equations. The student is asked to perform several tasks, one involves solving, one involves graphing and the final one compares the new equation with the original system.Gusmtsoe1.png

Strategies
Knowledge of algebraic rules is all that is needed to perform this exercise.
 * 1) For the equation, it is not literally necessary to "solve for y" or anything like that. At this stage the system is accepting any correct form, so this can increase speed since it is not necessary to simplify.
 * 2) When rules are followed correctly to solve a system, the result will have the original solution as a solution.
 * 3) In the case of substitution, the result will be a vertical or horizontal line at that solution. Recognizing this special case will increase speed.

Real-life Applications

 * 1) Understanding the process of algebra through these types of exercises can assist students with faster methods of being able to check answers in later math classes.