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

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.

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

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:

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

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:

Solve each system using the addition method. 1.

Solve each system using the addition method. 2.

Solve each system using the addition method. 3.

Solve each system using the addition method. 4.

Solve each system using the addition method. 5.

Solve each system using the addition method. 6.

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

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

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 _____________.

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 ___________________ = _____________

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:

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?