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Section 3.5 Solving Systems of Linear Equations in Two Variables by the Addition Method

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3.5 Lecture Guide: Solving Systems of Linear Equations in Two Variables by the Addition Method Objective 1: Solve a system of linear equations by the addition method.

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Addition Method: Step 1. Write both equations in the _________________ form. Example:

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Addition Method: Step 2. If necessary, multiply each equation by a constant so that the equations have one variable for which the coefficients are ____________ ____________. Example:

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Addition Method: Step 3. Add the new equations to ______________ a variable, and then solve the resulting equivalent equation. Example:

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Addition Method: Step 4. ______________ this value into one of the original equations, and solve for the other variable. The ordered pair obtained in Steps 3 and 4 is the solution. Example:

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Solve each system using the addition method. 1.

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Solve each system using the addition method. 2.

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Solve each system using the addition method. 3.

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Solve each system using the addition method. 4.

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Solve each system using the addition method. 5.

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Solve each system using the addition method. 6.

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7. Solve each system using either the substitution method or the addition method.

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8. Solve each system using either the substitution method or the addition method.

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9.After the first two algebra exams, one student had a mean score of 90 and range of 12. What were the scores on the two exams? (a) Identify the variables: Let x = the ____________ on one exam Let y = the ____________ on the other exam (b) Write the word equations: The ______________ of the two scores is 90. The ______________ of the two scores is _____________.

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9.After the first two algebra exams, one student had a mean score of 90 and range of 12. What were the scores on the two exams? (c) Translate the word equations into algebraic equations: ___________________ = 90 ___________________ = _____________

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9.After the first two algebra exams, one student had a mean score of 90 and range of 12. What were the scores on the two exams? (d) Solve this system of equations:

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9.After the first two algebra exams, one student had a mean score of 90 and range of 12. What were the scores on the two exams? (e) Write a sentence that answers the question. (f) Is this answer reasonable?

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