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CHAPTER_ppt_4_3

# CHAPTER_ppt_4_3 - 4.3 Solving Systems of Linear Equations...

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§ 4.3 Solving Systems of Linear Equations by Addition

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Martin-Gay, Beginning and Intermediate Algebra, 4ed 2 The Addition Method Another method that can be used to solve systems of equations is called the addition or elimination method . You multiply both equations by numbers that will allow you to combine the two equations and eliminate one of the variables.
Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Solve the following system of equations using the addition method. 6 x – 3 y = –3 and 4 x + 5 y = –9 Multiply both sides of the first equation by 5 and the second equation by 3. First equation, 5(6 x – 3 y ) = 5(–3) 30 x – 15 y = –15 Use the distributive property. Second equation, 3(4 x + 5 y ) = 3(–9) 12 x + 15 y = –27 Use the distributive property. The Addition Method Continued. Example :

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Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Combine the two resulting equations (eliminating the variable y ). 30 x – 15 y = –15 12 x + 15 y = –27 42 x = –42 x = –1 Divide both sides by 42. The Addition Method Continued. Example continued :
Martin-Gay, Beginning and Intermediate Algebra, 4ed 5 Substitute the value for x into one of the original equations.

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CHAPTER_ppt_4_3 - 4.3 Solving Systems of Linear Equations...

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