Library

3.8 Solving by Elimination

By Jennifer Pariseau
Last updated about 1 year ago
31 Questions
Note from the author:
OBJECTIVES & STANDARDS
Math Objectives
  • Solve systems of linear equations by elimination
  • Compare solution methods for systems of linear equations
Common Core Math Standards
  • Link to all CCSS Math
  • CCSS.PRACTICE.MP4
  • CCSS.HSA.REI.A.1
  • CCSS.HSA.REI.B.3
  • CCSS.HSA.REI.C.5
Personal Finance Objectives
  • Make cost-benefit decisions
  • Plan and budget for near-term savings goals
National Standards for Personal Financial Education
Saving
  • 9b: Identify strategies to manage psychological and emotional obstacles to saving
DISTRIBUTION & PLANNING
Distribute to students
  • Student Activity Packet
  • Application Problems
OBJECTIVES & STANDARDS
Math Objectives
  • Solve systems of linear equations by elimination
  • Compare solution methods for systems of linear equations
Common Core Math Standards
  • Link to all CCSS Math
  • CCSS.PRACTICE.MP4
  • CCSS.HSA.REI.A.1
  • CCSS.HSA.REI.B.3
  • CCSS.HSA.REI.C.5
Personal Finance Objectives
  • Make cost-benefit decisions
  • Plan and budget for near-term savings goals
National Standards for Personal Financial Education
Saving
  • 9b: Identify strategies to manage psychological and emotional obstacles to saving
DISTRIBUTION & PLANNING
Distribute to students
  • Student Activity Packet
  • Application Problems
Intro - Warm-Up
QUESTION OF THE DAY: Which savings strategy is most effective?
Write your answer to the question below. Then, compare your answer to the answer on the second slide. Finally, follow your teacher’s directions on how to answer the follow-up questions below. You may assume there are 30 days in a month for this saving example.

Which savings strategy is most effective:
  1. Saving $5 per day?
  2. Saving $35 per week?
  3. Saving $150 per month?

Why do you think the winning strategy is more effective than the others?

How can you compare these three savings strategies that all have different time frames?

What do you notice about the amount saved per month for each of the three saving strategies?

What strategy saves the most in a year? How much does it save?

What do you think the results of this study say about how much saving has to do with math and how much saving has to do with your mindset?

Learn It
Solving Systems by Elimination
So far, you have learned how to solve systems of equations by graphing and by using substitution. We will look at a third method here.
Like substitution, the elimination method is an algebraic method that allows you to find a numerical answer to a system of equations.


Solve the system of equations using elimination.



_______
Solve the system of equations using elimination.
x - 3y = 2
2x - 13= -3y
Solve the system of equations using elimination.
3x = 2 + 2y
3y - 4 = -2x
  1. Fill in the missing parts to solve the system of equations.
2x = 8 + 2y
0 = 4 - 3x - y

1 Rearrange:
2x - _______= 8
_______= 4

2 Multiply:
(2x - 2y = 8)
_______ (3x + y = 4)

3 Add:
2x - 2y = 8
_______+ 2y = _______

4 Solve:
8x = _______
x = _______

5 Substitute:
2(_______) - 2y = 8
-2y =_______
y =_______
6 Answer:
_______
2y + 2x = 10
2y + x = 7
Answer: _______
x + y = 4 -3x - y = 0
Answer: _______
y - 3x = 10 2y - x = -5
Answer: _______
3x - 2y = 2 5x - 5y = 10
Answer: _______
5x + 4y = -14 3x + 6y = 6
Answer : _______
2y = x + 1 -2x - y = 7
Answer: _______
3y = 2x
2y + x = 7
Answer: _______

For the following problems, choose the solving method that you think is most appropriate and state the reasons why you made that choice.There may be more than one method that works. You do NOT need to solve the problem.
y = 2x + 1
y = 6 - 3x

For the following problems, choose the solving method that you think is most appropriate and state the reasons why you made that choice.There may be more than one method that works. You do NOT need to solve the problem.
x + 3y = 7
2x + 3y = 11

For the following problems, choose the solving method that you think is most appropriate and state the reasons why you made that choice.There may be more than one method that works. You do NOT need to solve the problem.
3x - 2y = -7
2x + 5y = 8

For the following problems, choose the solving method that you think is most appropriate and state the reasons why you made that choice.There may be more than one method that works. You do NOT need to solve the problem.
3x - 2y = -7
2x + 5y = 8

Desmos! Card Sort: Linear Systems of Equations Go to Google Classroom for the Link :)
APPLICATION: Business Decisions and Solving by Elimination

Level 1

Sibling Savings
Leyla and her sister Maryam are excited to begin saving for a new bike they can share. Their aunt said that if they saved up enough money, she would split the cost with them and pay for half. The new bike will cost $110 total.
The girls concluded that they would have just enough if they saved the money from 2 days’ worth of Leyla’s paper route and 3 days’ worth of Maryam’s dog walking job. Maryam has to work a little more because her dog walking job pays $5 less than Leyla’s paper route. How much do the paper route and dog walking jobs each earn per day?
Write a system of equations to model this problem._______ _______
x=Leyla's Paper Route
y=Maryan's Dog Walking
Solve this system of equations using whichever method you choose. Show your work._______
How much do the paper route _______ and dog walking _______ earn the girls a day?

Would their wages be higher or lower if it actually took them 3 days of Leyla’s paper route and 5 days of Maryam’s dog walking job?

Choose whether you would use substitution or elimination to solve the following systems of equations and why.
x - 2y = -7
2x + 5y = 8

Choose whether you would use substitution or elimination to solve the following systems of equations and why.
5x - 3y = 16
3x + 6y = 18

Choose whether you would use substitution or elimination to solve the following systems of equations and why.
x  = 4y + 6
2x + y = 2

Choose whether you would use substitution or elimination to solve the following systems of equations and why.
2y = -4x - 14
2x + 10 = y

Choose whichever method you want to use to solve the following problems.

Sharon has three times the money saved as Robert. Together, they have $80. How much do they each have?
Sharon: _______
Robert: _______
Rebekah and Mohammad have $125 saved up already with their clothing business. For every shirt they sell, they make $12 and for every hat they make $9. How many of each did they sell if they sold 22 pieces of clothing and their total saved at the end of the day is $350, including the savings they started with?
Shirts Sold:_______
Hats Sold: _______