system of equations substitution eliminationgraphing q $100 q $200 q $300 q $400 q $500 q $100 q...

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System of Equations Substitu tion EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $100 Q $100 Q $100 Q $200 Q $200 Q $200 Q $200 Q $300 Q $300 Q $300 Q $300 Q $400 Q $400 Q $400 Q $400 Q $500 Q $500 Q $500 Q $500 Final Jeopardy Jeopardy Real life scenari os

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Page 1: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

System ofEquations

Substitution Elimination Graphing

Q $100

Q $200

Q $300

Q $400

Q $500

Q $100 Q $100Q $100 Q $100

Q $200 Q $200 Q $200 Q $200

Q $300 Q $300 Q $300 Q $300

Q $400 Q $400 Q $400 Q $400

Q $500 Q $500 Q $500 Q $500

Final Jeopardy

JeopardyReal life scenarios

Page 2: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

What is the solution to this system of equations?

Jeopardy

3 3

7

y x

y x

Page 3: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

(1,6)

Jeopardy

Page 4: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

A system of equations has been graphed at the right. What is the solution to this system of equations?

Jeopardy

Each tick mark = 1

Page 5: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

(3, 3)

Jeopardy

Page 6: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

(1, 2) is a solution to which system of equations?

Jeopardy

4 2)

3

y xa

y x

1)

3

y xc

y x

4 4)

8 6

y xb

y x

Page 7: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

1)

3

y xc

y x

Page 8: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Given the system of equations, what do you know about their solution?

Jeopardy

3 2

6 2

y x

y x

Page 9: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

There is no solution.The lines have the same.The lines are parallel.They lines will not intersect.

Jeopardy

Page 10: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

x y

-2 0

0 2

2 4

4 6

6 8

x y

-1 5

0 8

1 11

2 14

3 17

Each table represents a set of linear data. What is the solution to this system of equations?

Page 11: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

(-3, -1)

Jeopardy

x y

-4 -2

-3 -1

-2 0

0 2

2 4

4 6

6 8

x y

-3 -1

-1 5

0 8

1 11

2 14

3 17

Page 12: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Solve this system of equations by substitution:

Jeopardy

3

14 4

d t

d t

Page 13: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

(2, 6)

Page 14: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

Solve this system of equations by substitution:

1.5

12 2.5

d t

d t

Page 15: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

(3, 4.5)

Page 16: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

Solve this system of equations by substitution:

232 8

y x

y x

Page 17: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

(6, 4)

Jeopardy

Page 18: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

Solve this system of equations by substitution:

2 3

12

2

y x

y x

Page 19: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

(0, 2)

Jeopardy

Page 20: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Which system of equations if already set up to use the substitution method to solve for the solution?

Jeopardy

3 4 12)2 3 8

x ya

x y

12

3)3

64

y xb

y x

3 1 12)3 3 12

x yc

x y

Page 21: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

12

3)3

64

y xb

y x

Page 22: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

You want to use the elimination method to solve for the solution to this system of equations.

3 7 8

5 8 6

x y

x y

Tell how you can eliminate the y term.

Page 23: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

Multiply the first equation by -8 and the second equation by 7 and then add the equations.

Or

Multiply the first equation by 8 and the second equation by -7 and then add the equations

Or

Multiply the first equation by 8 and the second equation by 7 and then subtract the equations

Page 24: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

Solve this system of equations by elimination:

60

20

y x

y x

Page 25: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

(20, 40)

Page 26: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

Solve this system of equations by elimination:

6 5 20

6 10 25

x y

x y

Page 27: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

(-2.5, -1)

Page 28: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

Solve this system of equations by elimination:

15

22 1 10

x y

x y

Page 29: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

Infinitely many solutions because the two equations are the same line.

Page 30: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

Solve this system of equations by elimination:

12

31 1

02 6

x y

x y

Page 31: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

(1, 3)

Jeopardy

Page 32: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

What best describes the systems of equations shown in the graph below?

Jeopardy

graphing

Page 33: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

No Solution

graphing

Page 34: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Which of the following is true for a system of equations to have an intersection at exactly one point?

a.) Both equations must have the same slope. b.) Both equations must have the same slope and the

same y-intercept. c.) The equations must have different slopes and the y-

intercepts can be the same or different.

Jeopardy

graphing

Page 35: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

c.) The equations must have different slopes and the y-intercepts can be the same or different.

graphing

Page 36: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

What inequality statement is graphed at the right?

Jeopardy

graphing

Page 37: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

11

2y x

graphing

Page 38: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

The dark blue section represents the solution of a system of inequalities.

True or FalseThe points (4, 1) is in the solution set.

graphing

Page 39: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

False

graphing

Page 40: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

What inequality statement is graphed at the right?

graphing

Page 41: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

x < 2

Jeopardy

graphing

Page 42: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

A buffet has one price for adults and another for children.The Taylor family has two adults and three children, and their bill was $40.50. The Wong family has three adults and one child. Their bill was $38. Write a system of equations to determine the price for an adult and for a child?

real life scenarios

Page 43: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

2x + 3y = 40.50 3x + y = 38

real life scenarios

Page 44: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

Suppose your community center sells a total of 292 tickets for a basketball game. An adult ticket costs $3 and a student ticket costs $1. The sponsors collect $470 in total ticket sales. Write a system of equations to determine how many adult and student tickets were sold?

real life scenarios

Page 45: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

3a + s = 470 a + s = 292

real life scenarios

Page 46: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

real life scenarios

Two health clubs offer different plans for physical training. Fit Zone charges a $30 initial fee and an additional $10 for each hour of physical training. Ultra Strength charges an initial fee of $55 and an additional $5 for each hour of physical training.

Bill buys 10 hours of physical training. Determine which health club plan would cost less for Bill.

Page 47: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

real life scenarios

Page 48: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

real life scenarios

Two health clubs offer different plans for physical training. Fit Zone charges a $30 initial fee and an additional $10 for each hour of physical training. Ultra Strength charges an initial fee of $55 and an additional $5 for each hour of physical training.

Identify the hours of physical training when both plans cost an equal amount.

Page 49: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

real life scenarios

Page 50: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

real life scenarios

Two health clubs offer different plans for physical training. Fit Zone charges a $30 initial fee and an additional $10 for each hour of physical training. Ultra Strength charges an initial fee of $55 and an additional $5 for each hour of physical training.

Describe which plan costs less with respect to hours of physical training.

Page 51: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

real life scenarios

Page 52: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

Jeopardy

Complete the following statements:

1. A system of two linear equations has no solution if …2. A system of two linear equations has infinitely many solutions if …3. A system of two linear equations has exactly one solution if …

Page 53: System of Equations Substitution EliminationGraphing Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Jeopardy Real

1. The equations have different y-intercepts and the same slope (parallel lines)

2. The equations have the same y-intercept and the same slope (same lines)

3. The equations have different slopes and the same or different y-intercepts (intersecting lines)

Jeopardy