NAME ________________________________________________ DATE ____________________ PERIOD __________

SCORE __________ Practice A.3(H)

_____

1 Which region represents the solution to the

system of linear inequalities?

y ≥ -xy ≤ x - 2

y

xO A

B

C

D

A Region A

B Region B

C Region C

D Region D

2 Which region represents the solution to the

system of linear inequalities?

y ≥ 4 - 2xy ≤ -2 - 2x

y

xO

AB

C

F Region A

G Regions B and C

H Region C

J There is no solution.

Multi-Step Example

Graph the solution to the system of linear inequalities.

x + y < 4

-x + 2y ≥ 2

First, graph the lines x + y = 4 and -x + 2y = 2, the first as a

dashed line because x + y is strictly less than 4, the second as a

solid line because -x + 2y may equal 2.

Pick a test value that is not on either line. The point (0, 0) will work.

Substituting (0, 0) into the first inequality produces 0 + 0 < 4,

which is true, so (0, 0) is in the region of the solution to x + y < 4.

On the other hand, since -0 + 2.0 ≥ 2 is false, (0, 0) is not in

the solution region for -x + 2y ≥ 2. Thus, the solution is the

region depicted.

Graph the solution set of systems of two linear inequalities in two variables on the

coordinate plane.

y

xO

Mastering the TEKS, Algebra 1 33

Program: Mastering TEKs Component: ALG1First Round

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033_034B_ALG1_A_PRA_T_A3H_675315.indd 33 9/30/14 10:10 PM

NAME ________________________________________________ DATE ____________________ PERIOD __________

SCORE __________Practice A.3(H) (continued)

_____

P

3 For which value of k is the region depicted the

solution to the system?

2x + ky ≤ 10

y ≥ 4x - 2

y

xO

Record your answer and fill in the bubbles on

your answer document.

4 Which region represents the solution to the

system of linear inequalities?

y - x < 1

y ≤ -2

y

xO

AB

CD

A Region A

B Region B

C Region C

D Region D

5 The solution to the system of linear

inequalities

x + y < 10

2x - y ≥ 8

is going to be graphed. Which of the following

statements describes how the lines x + y = 10

and 2x - y = 8 should be drawn?

F Both lines should be solid.

G Both lines should be dashed.

H x + y = 10 should be solid and 2x - y

should be dashed.

J x + y = 10 should be dashed and 2x - y

should be solid.

6 Which region represents the solution to the

system of linear inequalities?

y ≥ 1 _

2 x - 1

y ≤ - 1 _

2 x - 1

y

xO

A

B

D

C

A Region A

B Region B

C Region C

D Region D

34

Program: Mastering TEKs Component: ALG1First Round

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Mastering the TEKS, Algebra 1

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