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Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111...

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Page 1: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.
Page 2: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Graphing Graphing SystemsSystems

1

3

2

4

5

1

3

2

4

5

1

3

2

4

5

1

3

2

4

5

11

33

22

44

55

Substitution Substitution MethodMethod

Elimination Elimination MethodMethod ApplicationsApplications Misc.Misc.

Page 3: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

Solve the system graphed.

Check Your Answer

Graphing for 1

Page 4: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

(2, 3)

Back to the Game Board

Graphing for 1

Page 5: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

If the equations of a system are graphed to be parallel lines, what is the solution?

Check Your Answer

Graphing for 2

Page 6: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

no solution

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Graphing for 2

Page 7: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

If a system has infinitely many solutions, what occurs when solving using the graphing method?

Check Your Answer

Graphing for 3

Page 8: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

You get coinciding lines.

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Graphing for 3

Page 9: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

Solve by graphing.

x + y = -1

y = 4x + 4

Check Your Answer

Graphing for 4

Page 10: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

(-1, 0)

Back to the Game Board

Graphing for 4

Page 11: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

State the system shown.

Check Your Answer

Graphing for 5

Page 12: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

y = 2x - 3

y = -x + 4

Back to the Game Board

Graphing for 5

Page 13: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

When is it best to use the substitution method when solving systems?

Check Your Answer

Substitution for 1

Page 14: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

When one of the equations is solved for one variable.

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Substitution for 1

Page 15: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

Solve by substitution.

y = 2x – 3

y = 6 – x

Check Your Answer

Substitution for 2

Page 16: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

(3, 3)

Back to the Game Board

Substitution for 2

Page 17: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Check Your Answer

Substitution for 3

Question:

Solve by substitution.

x = 3y + 5

2x + y = 3

Page 18: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

(2, -1)

Back to the Game Board

Substitution for 3

Page 19: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Check Your Answer

Substitution for 4

Question:

Solve by substitution.

5x – y = 2

y = 5x + 3

Page 20: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

no solution

Back to the Game Board

Substitution for 4

Page 21: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Check Your Answer

Substitution for 5

Question:

Solve by substitution.

3x – y = 11

y = 4x – 15

Page 22: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

(4, 1)

Back to the Game Board

Substitution for 5

Page 23: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

When is it best to use the elimination method for solving systems?

Check Your Answer

Elimination for 1

Page 24: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

When both equations are in standard form.

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Elimination for 1

Page 25: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

Solve by elimination.

x – 2y = 5

3y + 2y = –1

Check Your Answer

Elimination for 2

Page 26: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

(1, -2)

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Elimination for 2

Page 27: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

Solve by elimination.

3x – 5y = 0

–x + 2y = 2

Check Your Answer

Elimination for 3

Page 28: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

(10, 6)

Back to the Game Board

Elimination for 3

Page 29: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

Solve by elimination.

2x – 3y = –1

–6x + 9y = 3

Check Your Answer

Elimination for 4

Page 30: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

infinitely many solutions

Back to the Game Board

Elimination for 4

Page 31: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

Solve by elimination.

4x + 3y = –18

5x – 2y = –11

Check Your Answer

Elimination for 5

Page 32: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

(-3, -2)

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Elimination for 5

Page 33: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

Solve by graphing.

y > x – 3

y < 5 – x

Check Your Answer

Inequalities for 1

Page 34: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

Back to the Game Board

Inequalities for 1

Page 35: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

Solve by graphing.

y ≥ x

x < 3

Check Your Answer

Inequalities for 2

Page 36: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

Back to the Game Board

Inequalities for 2

Page 37: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Check Your Answer

Inequalities for 3

Question:

Solve by graphing.

2x – 3y > 12

y > (-1/2)x – 3

Page 38: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

Back to the Game Board

Inequalities for 3

Page 39: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

Is (3, -5) a solution to:

y > 2 – 7x

2x – 3y < 9

Check Your Answer

Inequalities for 4

Page 40: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

No; it fails the second inequality.

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Inequalities for 4

Page 41: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

State the system shown.

Check Your Answer

Inequalities for 5

Page 42: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

y ≥ –2

y < x – 1

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Inequalities for 5

Page 43: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

Solve for x.

3x – 7y = 12

2x + 2y = 5

Check Your Answer

Miscellaneous for 1

Page 44: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

x = 59/20

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Miscellaneous for 1

Page 45: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

Solve by graphing.

y = 3x + 2

6x – 2y = –4

Check Your Answer

Miscellaneous for 2

Page 46: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

infinitely many solutions

(the lines are coinciding)

Back to the Game Board

Miscellaneous for 2

Page 47: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:

Two numbers add to 9. One is 5 more than the other. What are the numbers?

Check Your Answer

Miscellaneous for 3

Page 48: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

7 and 2

x + y = 9

x = y + 5

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Miscellaneous for 3

Page 49: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Check Your Answer

Miscellaneous for 4

Question:

You buy 25 CD’s with some on sale at $10 and others at $15. If you spent $315, how many were on sale?

Page 50: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

12 were on sale

x + y = 25

10x + 15y = 315

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Miscellaneous for 4

Page 51: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Question:Graph

x > 1

y > 1

y ≤ 4 – 2x

Check Your Answer

Miscellaneous for 5

Page 52: Graphing Systems 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 1111 3333 2222 4444 5555 Substitution.

Answer:

Back to the Game Board

Miscellaneous for 5


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