Lesson 3: 6-3 Elimination Using Addition & Subtraction
Duration of Days: 4
Lesson Objective
Solve systems of equations by using elimination with addition.
Solve systems of equations by using elimination with subtraction.
What is an additive inverse? What is the additive inverse of 5y?
elimination
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A.REI.6 Solve systems of linear equations exactly, focusing on pairs of linear equations in two variables.
SAT questions related to systems: 4-3-16,1-3-18,1-3-9,2-3-2,8-3-18,6-4-11,7-3-3,1-3-11,7-4-11,1-4-19,8-3-10,2-4-29,2-3-20,3-3-9
Elimination using addition or subtraction uses the Addition and Subtraction Properties of Equality to combine two equations in a system of equations and eliminate one variable. After eliminating one variable, solve for the remaining variable. Then, substitute this value back into either original equation to find the value of the eliminated variable.
A hardware store earned $956.50 from renting ladders and power tools last week. The store charged customers for a total of 36 days for ladders and 85 days for power tools. This week the store charged 36 days for ladders, 70 days for power tools, and earned $829. How much does the store charge per day for ladders and for power tools?
When using elimination with subtraction to solve systems of equations, many students forget to distribute the negative sign over every term of the equation that is subtracted. Since subtraction is the same as adding the inverse, you might suggest that students change the signs of the terms and then add to eliminate the variable.
Kinesthetic Learners: Students may benefit from using concrete models to solve systems of equations with elimination. Have students write the terms of the equations on pieces of paper or use algebra tiles or other models to represent the equations. When they eliminate a variable, have them remove the model for that variable. The act of removing the terms should help them remember eliminating the variable.
Visual Learners: Have students find the missing value. The values represent the sums of each row and column. Hint: Let each symbol or set of symbols represent one variable.
Extension: Write two equations on the board with the constants missing. Have students find the missing constants that ensure the given solution. For example, write the system 3x + 2y = ?, 5x - 2y = ? and tell students that the solution is (1.5, 0.25).
Practice: Exercises 1 - 6
Exercises 40 - 46
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