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

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Presentation transcript:

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

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

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

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”.

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

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

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

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

Guided Practice

Independent Practice