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.

Question:

Solve the system graphed.

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Graphing for 1

Answer:

(2, 3)

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Graphing for 1

Question:

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

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Graphing for 2

Answer:

no solution

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Graphing for 2

Question:

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

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Graphing for 3

Answer:

You get coinciding lines.

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Graphing for 3

Question:

Solve by graphing.

x + y = -1

y = 4x + 4

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Graphing for 4

Answer:

(-1, 0)

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Graphing for 4

Question:

State the system shown.

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Graphing for 5

Answer:

y = 2x - 3

y = -x + 4

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Graphing for 5

Question:

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

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Substitution for 1

Answer:

When one of the equations is solved for one variable.

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Substitution for 1

Question:

Solve by substitution.

y = 2x – 3

y = 6 – x

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Substitution for 2

Answer:

(3, 3)

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Substitution for 2

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Substitution for 3

Question:

Solve by substitution.

x = 3y + 5

2x + y = 3

Answer:

(2, -1)

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Substitution for 3

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Substitution for 4

Question:

Solve by substitution.

5x – y = 2

y = 5x + 3

Answer:

no solution

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Substitution for 4

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Substitution for 5

Question:

Solve by substitution.

3x – y = 11

y = 4x – 15

Answer:

(4, 1)

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Substitution for 5

Question:

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

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Elimination for 1

Answer:

When both equations are in standard form.

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Elimination for 1

Question:

Solve by elimination.

x – 2y = 5

3y + 2y = –1

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Elimination for 2

Answer:

(1, -2)

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Elimination for 2

Question:

Solve by elimination.

3x – 5y = 0

–x + 2y = 2

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Elimination for 3

Answer:

(10, 6)

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Elimination for 3

Question:

Solve by elimination.

2x – 3y = –1

–6x + 9y = 3

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Elimination for 4

Answer:

infinitely many solutions

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Elimination for 4

Question:

Solve by elimination.

4x + 3y = –18

5x – 2y = –11

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Elimination for 5

Answer:

(-3, -2)

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Elimination for 5

Question:

Solve by graphing.

y > x – 3

y < 5 – x

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Inequalities for 1

Answer:

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Inequalities for 1

Question:

Solve by graphing.

y ≥ x

x < 3

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Inequalities for 2

Answer:

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Inequalities for 2

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Inequalities for 3

Question:

Solve by graphing.

2x – 3y > 12

y > (-1/2)x – 3

Answer:

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Inequalities for 3

Question:

Is (3, -5) a solution to:

y > 2 – 7x

2x – 3y < 9

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Inequalities for 4

Answer:

No; it fails the second inequality.

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Inequalities for 4

Question:

State the system shown.

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Inequalities for 5

Answer:

y ≥ –2

y < x – 1

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Inequalities for 5

Question:

Solve for x.

3x – 7y = 12

2x + 2y = 5

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Miscellaneous for 1

Answer:

x = 59/20

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Miscellaneous for 1

Question:

Solve by graphing.

y = 3x + 2

6x – 2y = –4

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Miscellaneous for 2

Answer:

infinitely many solutions

(the lines are coinciding)

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Miscellaneous for 2

Question:

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

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Miscellaneous for 3

Answer:

7 and 2

x + y = 9

x = y + 5

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Miscellaneous for 3

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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?

Answer:

12 were on sale

x + y = 25

10x + 15y = 315

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Miscellaneous for 4

Question:Graph

x > 1

y > 1

y ≤ 4 – 2x

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Miscellaneous for 5

Answer:

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Miscellaneous for 5