Unit 3 Summary
Class : Algebra 1 Honors
Unit 3: Systems of Equations – Chapter 8
I.
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Big Ideas:
Students will understand that systems of linear equations can be represented and solved using a
variety of strategies.
Students will understand how to apply their knowledge of systems of equations to interpret and
make judgments in real world situations.
Students will be able to recognize situations where a system of equations would be used to solve the
problem.
II.
Topics that will be covered:
1.
2.
3.
4.
5.
6.
7.
III.
Solving systems of equations by graphing
Solving systems of equations by substitution
Solving systems of equations by elimination
Consistent, independent, dependent, and inconsistent systems
Using systems of equations to solve real-life problems
Determine the best method for solving systems of equations
Solving systems of inequalities by graphing
Essential Questions:
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What is the best way to solve a particular system of equations?
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What is the significance of the solution to a system of linear equations?
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How do I know how many solutions a system of equations will have?
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What are the benefits of having different types of strategies to solve systems of equations related
to real-world situations?
IV.
Sample questions to answer by the end of the unit:
1. A bank teller is counting $20 bills and $10 bills. There are 16 bills that total $200. Write and solve a
system of equations to find the number of $20 bills and $10 bills.
2. Bob bought 8 hockey tickets for $59. Adult tickets cost $10 each and child tickets cost $3 each. How
many adult tickets did he buy?
3. The length of a rectangle is 2 centimeters longer than its width. The perimeter is 16 centimeters. What
are the length and width of the rectangle?
4. Which is the solution to the system of equations: 2x + y = 4
3x – y = -14
A. (-2, 8)
B. (-2, 0)
C. (2, 0)
D. (0, -2)
5. The concession stand sells pizza and drinks during football games. Jack bought 4 drinks and 6 slices of
pizza and paid $6.70. Amy bought 4 slices of pizza and 3 drinks and paid $4.65. What price is each drink
and each slice of pizza?
6. Students pay $2 per ticket and adults pay $5 per ticket. Although the stadium is filled to its capacity of
2000, 254 of those seats are given free of charge to band members, pep squad members, and faculty
members. The ticket-booth manager reports to the athletic director that the total income from the sale of
tickets for the current game is $5766. How many student and adult tickets were sold?
7. A father is 28 years older than his son. In 5 years the father will be 5 times as old as his son. How old is
each now?
8. The sum of two numbers is 17. The smaller number is 33 less than the greater number. Find the two
numbers.
Graph each of the following systems and then determine if they are independent, dependent, or
inconsistent.
9. 2x + y = 3
10. 4y = 2x – 12
-8x – 4y = 20
3x – 2y = 10
11. At the annual school fair for the scholarship fund, senior class sold cookies for $6 per box and brownies
for $8 per box. The goal for each senior was to sell at least $120 worth of cookies and brownies. However,
it was hoped that no one would have to sell more than 50 boxes. Write and graph a system of linear
inequalities to describe this situation. What are the reasonable domain and range for this situation? Find at
least 3 possible solutions to the system.
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