6-1: Graphing Systems of Equations

Solve the inequality: -7x < -9x + 14

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10% 10%

62%

19%

1. x < 22. x > 23. x < 74. x > 9

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Solve the inequality: w > -6

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55%

20%15%

10%

2

5

1. w > -152. w > -303. w > -12/5

4. w < 15

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Solve |3a – 2| < 4.

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10% 10%

20%

60%1. a > 2/3

2. a < 23. 3/2 < a < 4

4. -2/3 < a < 2

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Graph the solution set: -2/3 < a < 2

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0%

35%

15%

50%1. 2. 3. 4.

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Write an inequality, and then solve the following: Ten less than five times a number is greater than ten.

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25%

20%

15%

40%1. 5n > 10;n > 2

2. 5n – 10 > 10;n > 4

3. 5n – 10 < 10;n < 4

4. 5n < 10;n < 2

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Lori had a quarter and some nickels in her pocket, but she had less than $0.80. What is the greatest number of nickels she could have had?

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5%

20%

40%

35%

1. 12 nickels2. 11 nickels3. 10 nickels4. 9 nickels

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Which inequality does the graph below represent?

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15%

25%

20%

40%1. 3x – y < 12. -3x + y > 13. 2x – y > 34. -2x + y < 1

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6-1: Graphing Systems of Equations

In Algebra 1A, you graphed linear equationsNow

We will determine the number of solutions a system of linear equations has

Solve systems of linear equations by graphing

6-1: Graphing Systems of Equations

New Vocabulary System of Equations

A set of equations that all use the same variables Consistent

A system of equations that has at least one ordered pair that satisfies both equations

Independent A system of equations with exactly one solution

Dependent A system of equations that has an infinite number of solutions

Inconsistent A system of equations with no ordered pairs that satisfy both

equations

6-1: Graphing Systems of Equations

6-1: Graphing Systems of Equations

Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent The graphs are parallel, so

there is no solution. The system is inconsistent.

6-1: Graphing Systems of Equations

Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent The graphs intersect at

exactly one point, so there is exactly one solution. Thesystem is consistent andindependent.

Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent

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40%

5%

25%

30%1. Consistent and independent

2. Inconsistent3. Consistent and

dependent4. Cannot be

determined

2y + 3x = 6y = x – 1

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Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent

1. Consistent and independent

2. Inconsistent3. Consistent and

dependent4. Cannot be

determined

y = x + 4y = x – 1

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6-1: Graphing Systems of Equations

Assignment Page 338 Problems 1 – 6 and 10 – 15 (all)

6-1: Graphing Systems of Equations

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. y = 2x + 3

8x – 4y = -12The graphs coincide. There are infinitely many solutions of this system of equations.

6-1: Graphing Systems of Equations

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. x – 2y = 4

x – 2y = -2The graphs are parallel lines. Since they do not intersect, there are no solutions of this system of equations.

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

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25% 25%25%25%y = 2x + 3y = ½ x + 3

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1. One; (0, 3)2. No solution3. Infinitely many4. One; (3, 3)

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

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25% 25%25%25%x + 3y = 41/3 x + y = 0

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1. One; (0, 0)2. No solution3. Infinitely many4. One; (1, 3)

6-1: Graphing Systems of Equations

Real World Example Naresh rode 20 miles last week and plans to ride 35

miles per week. Diego rode 50 miles last week and plans to ride 25 miles per week. Predict the week in which Naresh and Diego will have ridden the same number of miles.

Number of miles ridden

Equals Number of miles per week

Times Number of weeks since week one

Plus Miles ridden in week one

Let y = the total number of miles ridden

Naresh y = 35 ● x + 20

Diego y = 25 ● x + 50

6-1: Graphing Systems of Equations

Graph the equations y = 35x + 20 y = 25x + 50

The graphs seem to intersectat the point (3, 125).

You can check by substituting(3, 125) for (x, y) in eachequation 125 = 35(3) + 20 125 = 25(3) + 50

Alex and Amber are both saving money for summer vacation. Alex has already saved $100 and plans to save $25 per week until the trip. Amber has $75 and plans to save $30 per week. In how many weeks will Alex and Amber have the same amount of money?

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25% 25%25%25%1. 225 weeks2. 7 weeks3. 5 weeks4. 20 weeks

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6-1: Graphing Systems of Equations

Assignment Page 338 Problems 7, 9, 17 – 25 (odds)