A.REI.D.12: Graphing Systems of Linear Inequalities 1

Regents Exam Questions A.REI.D.12: Graphing Systems of Linear Inequalities 1



Name: ________________________

A.REI.D.12: Graphing Systems of Linear Inequalities 1

1 Which graph represents the solution of y x + 3 and y -2x - 2?

1)

3)

2)

4)

2 Given: y + x > 2

y 3x - 2 Which graph shows the solution of the given set of inequalities?

1)

3)

2)

4)

1

Regents Exam Questions A.REI.D.12: Graphing Systems of Linear Inequalities 1



Name: ________________________

3 What is one point that lies in the solution set of the system of inequalities graphed below?

1) (7,0) 2) (3,0)

3) (0,7) 4) (-3,5)

4

Which

ordered

pair

is

not

in

the

solution

set

of

y

>

-

1 2

x

+

5

and

y

3x

-

2?

1) (5,3)

3) (3,4)

2) (4,3)

4) (4,4)

5 Which point is a solution to the system below? 2y < -12x + 4

1)

1,

1 2

2) (0,6)

y < -6x + 4

3)

-

1 2

, 5

4) (-3,2)

6

First consider the system of equations

y

=

-

1 2

x

+

1

and

y

= x - 5.

Then consider the system of inequalities

y

>

-

1 2

x

+

1

and

y

< x - 5.

When comparing the number

of solutions in each of these systems, which statement is

true?

1) Both systems have an infinite number of 3) The system of inequalities has more

solutions.

solutions.

2) The system of equations has more

4) Both systems have only one solution.

solutions.

2

Regents Exam Questions A.REI.D.12: Graphing Systems of Linear Inequalities 1



Name: ________________________

7 Determine if the point (0,4) is a solution to the system of inequalities graphed below. Justify your answer.

8 Graph the system of inequalities on the set of axes below:

y

-

3 4

x

+

5

3x - 2y > 4

Is (6,3) a solution to the system of inequalities? Explain your answer. 3

Regents Exam Questions A.REI.D.12: Graphing Systems of Linear Inequalities 1



Name: ________________________

9 On the set of axes below, graph the following system of inequalities: 2y + 3x 14

4x - y < 2

Determine if the point (1,2) is in the solution set. Explain your answer.

4

Regents Exam Questions A.REI.D.12: Graphing Systems of Linear Inequalities 1



Name: ________________________

10 Graph the following systems of inequalities on the set of axes below: 2y 3x - 16

y + 2x > -5

Based upon your graph, explain why (6,1) is a solution to this system and why (-6,7) is not a solution to this system.

5

Regents Exam Questions A.REI.D.12: Graphing Systems of Linear Inequalities 1



Name: ________________________

11 Solve the system of inequalities graphically on the set of axes below. Label the solution set S. y + 3x < 5

1 2x - y

Is the point (-5,0) in the solution set? Explain your answer.

6

Regents Exam Questions A.REI.D.12: Graphing Systems of Linear Inequalities 1



Name: ________________________

12 Solve the system of inequalities graphically on the set of axes below. Label the solution set S. 2x + 3y < 9

2y 4x + 6

Determine if the point (0,3) is a solution to this system of inequalities. Justify your answer.

7

Regents Exam Questions A.REI.D.12: Graphing Systems of Linear Inequalities 1



Name: ________________________

13 On the set of axes below, graph the following system of inequalities: 2x + y 8

y - 5 < 3x

Determine if the point (1,8) is in the solution set. Explain your answer.

8

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