Adapted from the Traveling Book Seller, Drew Polly, 2006

Systems of Linear Systems of Linear EquationsEquations

By Dylan NicolettiBy Dylan NicolettiSummit High SchoolSummit High School

Objectives

Questions

Credits

Objectives

– Using appropriate computation methods 1.2.a

– Use multiple forms of linear equations 2.1.b– Represent linear functions using a table,

graph equations, and convert from one form to another 2.1.c

– Solve equations for one variable in terms of another 2.4.c

– Solve systems of linear equations with two and three variables 2.5.c

Directions

• Use a piece of paper to record all attempts at each problem.

• If you get the wrong answer, look for your mistake and rewrite the problem with your correction so you have a fully written correct response.

• Have fun and remember, you are practicing for a great performance on your upcoming assessment.

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2

Questions

3

14

1 4 5

6 7 8 9 10

11 12 13 15Solving by Elimination

Solving by Substitution

Solving by Graphing

CreditsAll teachers and students at non-profit schools can use, revise, or adapt this game at will at no cost on the condition that all prior designers are

cited.

• Adapted from “The Traveling Georgia Artist” by Lloyd Rieber, The University of Georgia, May 20, 2003

• Adapted from “The Traveling Book Seller” by Drew Polly,

UNC-Charlotte

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That’s Correct!

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Sorry, that’s not correct!

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1) Graph the system of equations and select the ordered pair that represents the system’s solution.

• ( 2 , 8 )• ( -2 , 8 )• ( 2 , -8 )• ( -2 , -8 )

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23

42

yx

xy

2) Two linear equations that have the same slope but different y-intercepts will have the following solution.

• None• One• Infinitely Many• Not Enough Information

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3) By analysis or graphing, the following system has how many solutions?

• None• One• Infinitely Many• Two

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824

42

yx

xy

4) If you wanted to graph a system by graphing the equations in slope-intercept form, what would be your first step?

• Solve Each Equation for x• Solve Each Equation for y• Write Equations in Standard• Find the X-Intercept of Each

Line

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5) Linear equations with different slopes _________ have one solution.

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• Never• Sometimes• Always• It depends on the coefficients

6) Solve the following system using substitution.

• ( 0 , 2 )• ( 2 , 2 )• ( -2 , 0 )• ( 2 , 0 )

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2

42

yx

xy

7) Solve the following system using substitution.

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• ( 2 , 0 )• ( 0 , 2 )• ( -2 , 0 )• ( 0 , 0 )

2

22

yx

yx

8) Find a and b so that ( 2 , 1 ) is a solution the system.

• a = 1 and b = -4• a = -1 and b = -4• a =-1 and b = 4• No solutions

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3

2

axy

byax

9) In the following system, which equation and what variable would you solve for?

• Equation 1 for y• Equation 1 for x• Equation 2 for x• Equation 2 for y

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43

374

yx

yx

10) The total number of points you can earn on a math test is 200 points. Your grade is 85% and you answered 42 problems correctly. Each problem is worth either 3 points or 5 points. How many 5-point problems did you answer correctly?

• 22• 29• 30

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11) Solve the following system using elimination.

• ( 4 , -5 )• ( 4 , 5 )• ( 2 , -3 )• ( -3 , 2 )

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9

1

yx

yx

12) Solve the following system using elimination.

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• ( 8 , 2 )

• ( 8 , 4 )

• ( 8 , 6 )

• ( 8 , 8 )

3623

275

yx

yx

13) Tell whether the system has one solution, nosolution , or infinitely many solutions.

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• No Solutions• Infinitely Many• One • Sometimes it has none

443

225

yx

yx

14) A store sells recordable compact discs in packs of 5 for $5 and packs of 10 for $8. You but 45 discs for $37. How many of each type of pack did you buy?

• 1 pack of 5; 4 packs of 10• 8 packs of 5; 1 pack of 10• 3 packs of 5; 3 packs of 10• 4 packs of 5; 1 pack of 10

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15) Your school band is performing a concert. Tickets for the concert cost $3 for students and $5 for adults. A total of 125 people attend the concert. Ticket sales total $475. How many students and adults are at the concert.

• 50 students; 75 adults• 85 students; 40 adults• 75 students; 50 adults

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