Lesson 4: 6-4 Elimination Using Multiplication
Duration of Days: 4
Lesson Objective
Solve systems of equations by using elimination with multiplication.
Solve real-world problems involving systems of equations.
What are the benefits of having different strategies for solving systems of equations?
What is a least common multiple (LCM)? What is the LCM of 6 and 7?
A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
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
When the coefficients of one of the variables are neither the same nor additive inverses in a system of equations elimination using multiplication can be used to solve the system. Multiply one or both equations by a number to get the equations to have the same coefficient. Then solve the system using elimination using addition or subtraction.
A fishing boat travels 10 miles downstream in 30 minutes. The return trip takes the boat 40 minutes. Find the rate in miles per hour of the boat in still water.
When using elimination with multiplication, many students forget to multiply each term on both sides of the equation by the number. Suggest that they include an extra step in the solutions that shows the multiplication:
3x + 2y = 7
2x - 7y = -12
?
2(3x + 2y) = 2(7)
-3(2x - 7y) = -3(-12)
If students have trouble solving Exercises 1–4, then suggest that they form groups of two or three to discuss the best strategy for solving each problem and then work through the solution together. Encourage all students to participate and remind students to check their solutions.
Practice: Exercises 1 - 6
Exercises 34-38
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