Chapter 4: System of Equations and Inequalities Section 4.4: Solving Linear Systems Using the Addition Method.

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Presentation transcript:

Chapter 4: System of Equations and Inequalities Section 4.4: Solving Linear Systems Using the Addition Method

Goal: To solve a linear system in two variables by addition

Section 4.4: Solving Linear Systems Using the Addition Method Elimination method – eliminate one of the variables by adding the equations. When you add two true equations, the result is a new equation that is also true

Section 4.4: Solving Linear Systems Using the Addition Method Example 3 Use the elimination method to solve the system of equations x + 2y = 10 -x – y = -6

Section 4.4: Solving Linear Systems Using the Addition Method Sometimes adding the two equations will not eliminate either variable. You may use multiplication to write an equivalent equation so that one of the variables has opposite coefficients in both equations. When you multiply an equation by a nonzero number, the new equation is equivalent to the original equation

Section 4.4: Solving Linear Systems Using the Addition Method Example 4 Use the elimination method to solve the system of equations 2x + 3y = 12 5x – 2y = 11

Section 4.4: Solving Linear Systems Using the Addition Method If you add two equations and the result is an equation that is: NEVER true The system in inconsistent ALWAYS true The system is consistent and dependent

Section 4.4: Solving Linear Systems Using the Addition Method Example 5 Use the elimination method to solve the system of equations -3x + 5y = 12 6x – 10y = -21

Section 4.4: Solving Linear Systems Using the Addition Method Example 6 Use the elimination method to solve the system of equations 0.01x y = x + 0.4y = 1.8

Section 4.4: Solving Linear Systems Using the Addition Method Homework Practice Exercises: Pg. 162 #2-28 (even)