Ch.6 Systems Of Linear Equations And Test Bank + Answers 5e - Test Bank | College Algebra 5e by Young by Cynthia Y. Young. DOCX document preview.

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Ch.6 Systems Of Linear Equations And Test Bank + Answers 5e

College Algebra, 5e (Young)

Chapter 6 Systems of Linear Equations and Inequalities

6.4 Systems of Linear Inequalities in Two Variables

1) Graph the linear inequality.

y is lesser than or equal to x minus 1.

An inequality is graphed on an x y coordinate plane. Both the axes range from negative 6 to 6, in increments of 1. A solid line slopes upward through (0, negative 1) and (1, 0). The region to the right of the solid line is shaded.

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a linear inequality in two variables.

2) Graph the linear inequality.

y is greater than one-half times x plus 1.

A)

An inequality is graphed on an x y coordinate plane. Both the axes range from negative 6 to 6, in increments of 1. A dotted line slopes upward through (negative 2, 0) and (0, 1). The region above the dotted line is shaded.

B)

An inequality is graphed on an x y coordinate plane. Both the axes range from negative 6 to 6, in increments of 1. A solid line slopes upward through (negative 2, 0) and (0, 1). The region above the solid line is shaded.

C)

An inequality is graphed on an x y coordinate plane. Both the axes range from negative 6 to 6, in increments of 1. A dotted line slopes upward through (negative 2, 0) and (0, 1). The region below the dotted line is shaded.

D)

An inequality is graphed on an x y coordinate plane. Both the axes range from negative 6 to 6, in increments of 1. A solid line slopes upward through (negative 2, 0) and (0, 1). The region below the solid line is shaded.

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a linear inequality in two variables.

3) Match the graph to the linear inequality.

An inequality is graphed on an x y coordinate plane. Both the axes range from negative 6 to 6, in increments of 1. A dotted line slopes upward through (0, negative 5) and (2, 0). The region to the right of the dotted line is shaded.

A) 5 times x minus 2 times y is greater than 10.

B) 5 times x minus 2 times y is greater than or equal to 10.

C) 5 times x plus 2 times y is greater than 10.

D) 5 times x minus 2 times y is greater than or equal to 10.

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a linear inequality in two variables.

4) Graph the system of inequalities.

Two equations read, y is greater than or equal to 3 times x minus 1; y is lesser than or equal to negative 3 times x plus 1.

Two inequalities are graphed on an x y coordinate plane. Both the axes range from negative 6 to 6, in increments of 0.5. The first inequality is a solid line that slopes upward through (negative 2, negative 6), (0, negative 1), and (0.2, 0). The second inequality is a solid line that slopes downward through (negative 2, 6), (0, 1), and (0.2, 0). The region to the left of the first solid line in the second quadrant and to the left of the second solid line in the third quadrant, is shaded.

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

5) Graph the system of inequalities.

Two equations read, y is greater than or equal to 3 times x minus 1; y is lesser than or equal to negative 3 times x plus 1.

A)

Two inequalities are graphed on an x y coordinate plane. Both the axes range from negative 6 to 6, in increments of 0.5. The first inequality is a solid line that slopes upward through (negative 2, negative 6), (0.2, 0), and (2, 4). The second inequality is a solid line that slopes downward through (negative 2, 6), (0.1, 0), and (2, negative 4). The region to the left of the first solid line in the third quadrant and to the left of the second solid line in the second quadrant, is shaded.

B)

Two inequalities are graphed on an x y coordinate plane. Both the axes range from negative 2 to 2, in increments of 0.25. The first inequality is a solid line that slopes downward through (negative 1, 2), (negative 0.25, 0), and (0, negative 1). The second inequality is a solid line that slopes downward through (negative 0.5, 2), (0.25, 0), and (1, negative 2). The region between the solid lines, is shaded

C)

Two inequalities are graphed on an x y coordinate plane. Both the axes range from negative 2 to 2, in increments of 0.25. The first inequality is a solid line that slopes upward through (negative 0.25, negative 1.5), (0, negative 1), and (0.3, 0). The second inequality is a solid line that slopes downward through (negative 0.25, 1.5), (0, 1), and (0.3, 0). The region to the right of the first solid line in the third and fourth quadrant and to the left of the second solid line in the fourth quadrant, is shaded.

D)

Two inequalities are graphed on an x y coordinate plane. Both the axes range from negative 6 to 6, in increments of 0.5. The first inequality is a solid line that slopes upward through (negative 2, negative 4), (negative 0.5, 0), and (2, 6). The second inequality is a solid line that slopes downward through (negative 2, 4), (negative 0.5, 0), and (2, negative 6). The region to the right of the first solid line in the first quadrant and to the right of the second dotted line in the fourth quadrant, is shaded.

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

6) Match the graph to the system of inequalities.

Two inequalities are graphed on an x y coordinate plane. Both the axes range from negative 5 to 5, in increments of 0.5. The first inequality is a solid line that slopes upward through (negative 5, negative 2), (negative 2, 0), and (0, 2). The second inequality is a solid line that slopes upward through (negative 3, negative 4), (0, negative 2), and (2, 0). The region between the solid lines, is shaded

A)

Two equations read, y is greater than or equal to negative x minus 2; y is lesser than or equal to negative x plus 2.

B)

Two equations read, y is greater than x minus 2; y is lesser than x plus 2.

C)

Two equations read, y is greater than or equal to x minus 2; y is lesser than or equal to x plus 2.

D)

Two equations read, y is lesser than or equal to x minus 2; y is greater than or equal to negative x plus 2.

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

7) Graph the system of inequalities.

Three equations read, x minus 4 times y is lesser than or equal to negative 8; y is lesser than or equal to 3; x is greater than or equal to negative 3.

Three inequalities are graphed on an x y coordinate plane. Both the axes range from negative 5 to 5, in increments of 0.5. The first inequality is a solid upward sloping line that passes through (0, 2) and (4, 3). The second inequality is a solid horizontal line that passes through (0, 3). The third inequality is a solid vertical line that passes through (negative 3, 0). The triangular region above the first line and between the second and third lines, is shaded.

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

8) Graph the system of inequalities.

Three equations read, 4 times x plus y is lesser than or equal to 8; y is greater than or equal to 3; x is greater than or equal to negative 1.

A)

Three inequalities are graphed on an x y coordinate plane. Both the axes range from negative 5 to 5, in increments of 0.5. The first inequality is a solid downward sloping line that passes through (1, 4) and (2, 0). The second inequality is a solid horizontal line that passes through (0, 3). The third inequality is a solid vertical line that passes through (negative 1, 0). The region below the second line and between the first and third lines, is shaded.

B)

Three inequalities are graphed on an x y coordinate plane. Both the axes range from negative 4 to 4, in increments of 0.5. The first inequality is a solid upward sloping line that passes through (0, 2) and (4, 3). The second inequality is a solid horizontal line that passes through (0, negative 1). The third inequality is a solid vertical line that passes through (negative 3, 0). The region below the first line and between the second and third lines, is shaded.

C)

Three inequalities are graphed on an x y coordinate plane. Both the axes range from negative 5 to 5, in increments of 0.5. The first inequality is a solid upward sloping line that passes through (0, 2) and (4, 3). The second inequality is a solid horizontal line that passes through (0, 3). The third inequality is a solid vertical line that passes through (negative 3, 0). The triangular region above the first line and between the second and third lines, is shaded.

D)

Three inequalities are graphed on an x y coordinate plane. Both the axes range from negative 7 to 7, in increments of 1. The first inequality is a solid downward sloping line that passes through (0, 7) and (2, 0). The second inequality is a solid horizontal line that passes through (0, 3). The third inequality is a solid vertical line that passes through (negative 1, 0). The region above the second line and between the first and third lines, is shaded.

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

9) Match the graph to the system of inequalities.

Three inequalities are graphed on an x y coordinate plane. Both the axes range from negative 5 to 5, in increments of 0.5. The first inequality is a solid upward sloping line that passes through (0, 2) and (4, 3). The second inequality is a solid horizontal line that passes through (0, 3). The third inequality is a solid vertical line that passes through (negative 3, 0). The triangular region above the first line and between the second and third lines, is shaded.

A)

Three equations read, x minus 4 times y is lesser than or equal to negative 8; y is lesser than or equal to 3; x is greater than or equal to negative 3.

B)

Three equations read, 4 times x plus y is lesser than or equal to 8; y is lesser than or equal to 3; x is greater than or equal to negative 1.

C)

Three equations read, 4 times x plus y is lesser than or equal to 8; y is greater than or equal to 3; x is greater than or equal to negative 1.

D)

Three equations read, x minus 4 times y is greater than or equal to negative 8; y is greater than or equal to negative 1; x is greater than or equal to negative 3.

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

10) Graph the system of inequalities.

Four equations read, 6 times x plus 2 times y is greater than or equal to 3; x plus y is greater than or equal to 2; y is greater than or equal to 1; x is greater than or equal to 0.

Four inequalities are graphed on an x y coordinate plane. Both the axes range from negative 4 to 4, in increments of 0.5. The first inequality is a solid downward sloping line that passes through (0, 2) and (2, 0). The second inequality is a solid downward sloping line that passes through (0, 1.5) and (0.5, 0). The third inequality is a solid horizontal line that passes through (0, 1). The fourth inequality is a solid vertical line that passes through (0, 3). The region to the right of the first line, and between the third and fourth lines, is shaded.

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

11) Graph the system of inequalities.

Four equations read, 4 times x minus y is lesser than 2; x plus 3 times y is lesser than 6; y is greater than 1; x is greater than negative 2.

A)

Four inequalities are graphed on an x y coordinate plane. Both the axes range from negative 2 to 2, in increments of 0.25. The first inequality is a dotted upward sloping line that passes through (0, negative 2) and (1, negative 1.75). The second inequality is a dotted downward sloping line that passes through (0, 2) and (0.5, 0). The third inequality is a dashed horizontal line that passes through (0, 1). The fourth inequality is a solid vertical line that passes through (0, 0). The region to the left of the second line, above the first line, and between the third and fourth lines, is shaded.

B)

Four inequalities are graphed on an x y coordinate plane. Both the axes range from negative 3 to 3, in increments of 0.5. The first inequality is a dotted upward sloping line that passes through (0, negative 2) and (0.5, 0). The second inequality is a dotted downward sloping line that passes through (0, 2) and (3, 1). The third inequality is a dashed horizontal line that passes through (0, 1). The fourth inequality is a dashed vertical line that passes through (negative 2, 0). The region to the left of the first line, above the third line, and between the second and fourth lines, is shaded.

C)

Four inequalities are graphed on an x y coordinate plane. Both the axes range from negative 3 to 3, in increments of 0.5. The first inequality is a dotted upward sloping line that passes through (negative 0.5, 0) and (0, 2). The second inequality is a dotted downward sloping line that passes through (0, 2) and (3, 1). The third inequality is a dashed horizontal line that passes through (0, 1). The fourth inequality is a dashed vertical line that passes through (negative 1, 0). The region to the left of the first line, above the third line, and between the second and fourth lines, is shaded.

D)

Four inequalities are graphed on an x y coordinate plane. Both the axes range from negative 3 to 3, in increments of 0.5. The first inequality is a dotted upward sloping line that passes through (negative 2, negative 2.5) and (0, negative 2). The second inequality is a dotted downward sloping line that passes through (0, 2) and (0.5, 0). The third inequality is a dashed horizontal line that passes through (0, 1). The fourth inequality is a dashed vertical line that passes through (negative 2, 0). The region above the first line, to the left of the second line, and between the third and fourth lines, is shaded.

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

12) Match the graph to the system of inequalities.

Three inequalities are graphed on an x y coordinate plane. Both the axes range from negative 3 to 3, in increments of 0.5. The first inequality is a solid downward sloping line that passes through (0, 2) and (2, 0). The second inequality is a solid downward sloping line that passes through (0, 1.5) and (0.5, 0). The third inequality is a solid horizontal line that passes through (0, 1). The region below the third line and between the first and second lines, is shaded.

A)

Four equations read, 3 times x plus 2 times y is lesser than or equal to 6; x minus y is greater than or equal to 2; y is lesser than or equal to 0; x is greater than or equal to 0.

B)

Four equations read, 3 times x plus 2 times y is greater than or equal to 6; x minus y is lesser than or equal to 2; y is greater than or equal to 0; x is greater than or equal to 0.

C)

Four equations read, 6 times x plus 2 times y is greater than or equal to 3; x plus y is lesser than or equal to 2; y is lesser than or equal to 1; x is greater than or equal to 0.

D)

Four equations read, 6 times x plus 2 times y is greater than or equal to 3; x plus y is greater than or equal to 2; y is greater than or equal to 1; x is greater than or equal to 0.

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

13) Employ the following supply and demand equations.

table ( (Demand P = 205 - 0.06x)(Supply P = 95 + 0.06x) )

Write a system of linear inequalities corresponding to the consumer surplus.

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

14) Employ the following supply and demand equations.

table ( (Demand P = 261 - 0.04x)(Supply P = 55 + 0.09x) )

Write a system of linear inequalities corresponding to the consumer surplus.

A) P ≥ 261 - 0.04x; P ≥ 198; x ≥ 0

B) P ≤ 55 + 0.09x; P ≤ 198; x ≥ 0

C) P ≤ 261 - 0.04x; P ≥ 198; x ≥ 0

D) P ≥ 261 - 0.04x; P ≤ 198; x ≥ 0

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

15) Employ the following supply and demand equations.

table ( (Demand P = 246 - 0.08x)(Supply P = 67 + 0.09x) )

Write a system of linear inequalities corresponding to the producer surplus.

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

16) Employ the following supply and demand equations.

table ( (Demand P = 122 - 0.05x)(Supply P = 52 + 0.04x) )

Write a system of linear inequalities corresponding to the producer surplus.

A) P ≥ 122 - 0.05x; P ≥ 83; x ≥ 0

B) P ≥ 122 - 0.05x; P ≥ 83

C) P ≤ 52 + 0.04x; P ≥ 83; x ≥ 0

D) P ≥ 52 + 0.04x; P ≤ 83; x ≥ 0

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

17) Graph the system of inequalities.

y > 2x - 3

y < - (1/3)x + 5

y ≥ 2

Three inequalities are graphed on an x y coordinate plane with equally spaced gridlines. Both the axes range from negative 5 to 5, in increments of 1. The first inequality is a dotted upward sloping line that passes through (0, negative 1.5) and (0.8, 0). The second inequality is a solid downward sloping line that passes through (0, 1.5) and (5, 0.9). The third inequality is a solid horizontal line that passes through (0, 1). The region to the left of the first line and between the second and third lines, is shaded.

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

18) Find the solution to the system of inequalities.

2x + 4y < 7

4y ≥ 15 - 2x

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

19) Find the solution to the system of inequalities.

5x + 2y < 5

2y < 13 - 5x

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 04

Learning Objective: Graph a system of linear inequalities in two variables.

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Chapter Number:
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Created Date:
Aug 21, 2025
Chapter Name:
Chapter 6 Systems Of Linear Equations And Inequalities
Author:
Cynthia Y. Young

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