1. Introduction to Systems of Equations and Identifying the Number of Solutions
Lesson 5

2. Standards and Objectives
A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
SWBAT Determining if a Systems of Equations has Infinite Solutions, One Solution or No Solutions

3. What is a System of Equations
A "system" of equations is a set of two or more equations with a same set of unknowns.

4. Steps
1. Rearrange your equations to slope-intercept form (y = mx + b) 2. Compare the slopes represented by “m” 3. Compare the y-intercepts represented by “b”.

5. Types of Solutions Number of Solutions Slopes Y-intercepts Graphs
Exactly One
Different
Same or different
Intersecting lines
None
Same
Distinct parallel lines
Infinite
Collinear

6. Example 1
Determine the number of solutions for the system of equations
2x + 3y = -3 and 4x +6y = -6

7. Example 2
Determine the number of solutions for the system of equations 3x = 6y – 4 and 6y = 3x + 12

8. Example 3
Determine the number of solutions for the system of equations 5 = 5y + x and 7x -3y = 9

9. Guided Practice

10. Independent Practice