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Systems of Linear Equations. By Dylan Nicoletti Summit High School. Objectives. Questions. Credits. Objectives. Using appropriate computation methods 1.2.a Use multiple forms of linear equations 2.1.b

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systems of linear equations

Systems of Linear Equations

By Dylan Nicoletti

Summit High School

Objectives

Questions

Credits

Adapted from the Traveling Book Seller, Drew Polly, 2006

objectives
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
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.

questions
Questions

Solving by Graphing

1

2

3

4

5

Solving by Substitution

6

7

8

9

10

Solving by Elimination

11

12

13

14

15

Question Page

slide5

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

Question Page

that s correct
That’s Correct!

Question Page

graph the system of equations and select the ordered pair that represents the system s solution
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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slide9
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
3) By analysis or graphing, the following system has how many solutions?

None

One

Infinitely Many

Two

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slide11
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
5) Linear equations with different slopes _________ have one solution.
  • Never
  • Sometimes
  • Always
  • It depends on the coefficients

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6 solve the following system using substitution
6) Solve the following system using substitution.

( 0 , 2 )

( 2 , 2 )

( -2 , 0 )

( 2 , 0 )

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7 solve the following system using substitution
7) Solve the following system using substitution.
  • ( 2 , 0 )
  • ( 0 , 2 )
  • ( -2 , 0 )
  • ( 0 , 0 )

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8 find a and b so that 2 1 is a solution the system
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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9 in the following system which equation and what variable would you solve for
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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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
11) Solve the following system using elimination.

( 4 , -5 )

( 4 , 5 )

( 2 , -3 )

( -3 , 2 )

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12 solve the following system using elimination
12) Solve the following system using elimination.
  • ( 8 , 2 )
  • ( 8 , 4 )
  • ( 8 , 6 )
  • ( 8 , 8 )

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13 tell whether the system has one solution no solution or infinitely many solutions
13) Tell whether the system has one solution, nosolution , or infinitely many solutions.
  • No Solutions
  • Infinitely Many
  • One
  • Sometimes it has none

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slide21

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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slide22

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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