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messersmith_power_introductory_algebra_1e_ch4_7_10

Putting It All Together What are your objectives? How can you accomplish each objective? 1 Review the concepts of Sections 4.1–4.3 • Understand the summary for Choosing Between Substitution and the Elimination Method to Solve a System, and write it in your own words. • Complete the You Try. Read the explanations, follow the examples, take notes, and complete the You Try. 1 Review the Concepts of Sections 4.1–4.3 We have learned three methods for solving systems of linear equations: 1) Graphing 2) Substitution 3) Elimination How do we know which method is best for a particular system? We will answer this question by summarizing what we have learned so far. First, solving a system by graphing is the least desirable of the methods. The point of intersection can be diffi cult to read, especially if one of the numbers is a fraction. But, the graphing method is important in certain situations and is one you should know. Summary Choosing Between Substitution and the Elimination Method to Solve a System 1) If at least one equation is solved for a variable and contains no fractions, use substitution. 5x 2y 8 x 4y 16 2) If a variable has a coeffi cient of 1 or 1, you can solve for that variable and use substitution. 4x y 10 3x 8y 7 Or, leave each equation in the form Ax By C and use elimination. Either approach is good and is a matter of personal preference. 3) If no variable has a coeffi cient of 1 or 1, use elimination. 4x 5y 3 6x 8y 11 Remember, if an equation contains fractions or decimals, begin by eliminating them. Then, decide which method to use following the guidelines listed here. In-Class Example Decide which method to use to solve each system, substitution or elimination, and explain why this method was chosen. Then, solve the system. a) 5x 2y 2 y 3x 3 b) x 5y 10 7x 3y 6 c) 2x 6y 1 3x 4y 9 Answer: a) substitution; (4, 9) b) substitution or elimination; (0, 2) c) elimination: a5, 3 2 b www.mhhe.com/messersmith Putting It All Together 271


messersmith_power_introductory_algebra_1e_ch4_7_10
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