AnswersMathematics ISolving Systems of Linear Inequalities

Solving Systems of Linear Inequalities — Quiz Answers

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1
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Which ordered pair makes both inequalities true? y is less than or equal to negative x plus 1 y is greater than x

A
negative 3 comma 5
B
negative 2 comma 2
C
0 comma negative 1
D
negative 1 comma negative 3
2
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Which system of linear inequalities is represented by the graph?

A
y is greater than or equal to x minus 2 and y is less than or equal to x plus 1
B
y is less than x minus 2 and y is greater than x plus 1
C
y is less than or equal to x minus 2 and y is greater than or equal to x plus 1
D
y is greater than x minus 2 and y is less than x plus 1
3

Which ordered pairs are in the solution set of the system of linear inequalities? y is greater than or equal to negative 1 half x y is less than 1 half x plus 1

A
5 comma negative 2 , 3 comma 1 , 4 comma 2
B
5 comma negative 2 , 3 comma negative 1 , 4 comma negative 3
C
5 comma negative 2 , 3 comma 1 , negative 4 comma 2
D
5 comma negative 2 , negative 3 comma 1 , 4 comma 2
4

Which graph shows the solution to the system of linear inequalities? y is greater than or equal to 2 x plus 1 y is less than or equal to 2 x minus 2

A
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 7 to 3 in increments of 1. The first line is solid and goes through the points (negative 2 comma negative 3) and (0 comma 1). Everything to the left and right of the solid line is shaded in different colors. The second line is dashed goes through the points (0 comma negative 2) and (1 comma 0). Everything to the left and right of the dashed line is shaded in different colors.
B
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 7 to 3 in increments of 1. There are 2 solid lines on the graph. The first solid line goes through the points (-2,-3) and (0, 1). Everything to the left of the solid line is shaded. The second solid line goes through the points (0,-2) and (1,1). Everything to the right of the solid line is shaded.
C
Image with description A coordinate plane with the x-axis labeled from −5 to 5 and the y-axis labeled from −7 to 3. Two lines divide the plane. A solid blue line with arrowheads passes through approximately (-2, −3) and (0, 1). The region to the left of this solid blue line is shaded light blue. A dashed red line with arrowheads passes through approximately (0, −2) and (1, 1). The region to the right of this dashed red line is shaded tan.
D
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 7 to 3 in increments of 1. There are 2 solid lines on the graph. The first solid line goes through the points (negative 2 comma negative 3) and (0 comma 1). Everything to the left and the right of the solid line is shaded in different colors. The second solid line goes through the points (0 comma negative 2) and (1 comma 0). Everything to the left and right of the solid line is shaded in a different color.
5

Which graph shows the solution to the system of linear inequalities? x minus 4 y is less than or equal to 4 y is less than x plus 1

A
Image with description On a coordinate plane, 2 straight lines are shown. The scale on the x and y axes ranges from negative 5 to 5. The first solid line has a positive slope and goes through the points (0 comma negative 1) and (4 comma 0). Everything to the left of the solid line is shaded. The second dashed line also has a positive slope and goes through the points (negative 1 comma 0) and (0 comma 1). Everything to the right of the dashed line is shaded.
B
Image with description On a coordinate plane, 2 straight lines are shown. The scale on the x and y axes ranges from negative 5 to 5. The first solid line has a positive slope and goes through the points (0 comma negative 1) and (4 comma 0). Everything to the left of the solid line is shaded. The second solid line also has a positive slope and goes through the points (negative 1 comma 0) and (0 comma 1). Everything to the right of the dashed line is shaded.
C
Image with description On a coordinate plane, 2 straight lines are shown. The scale on the x and y axes ranges from negative 5 to 5. The first solid line has a positive slope and goes through the points (0 comma negative 1) and (4 comma 0). Everything below the solid line is shaded. The second dashed line also has a positive slope and goes through the points (negative 1 comma 0) and (0 comma 1). Everything below the dashed line is shaded.
D
Image with description On a coordinate plane, 2 straight lines are shown. The scale on the x and y axes ranges from negative 5 to 5. The first solid line has a positive slope and goes through the points (0 comma negative 1) and (4 comma 0). Everything to the left of the solid line is shaded. The second dashed line also has a positive slope and goes through the points (negative 1 comma 0) and (0 comma 1). Everything to the left of the dashed line is shaded.
6

Which system of linear inequalities has the point 3 comma negative 2 in its solution set?

A
y is less than negative 3 y is greater than or equal to 2 thirds x minus 4 Image with description On a coordinate plane, 2 straight lines are shown. The first dashed line is parallel to the x-axis at y = negative 3. Everything below the dashed line is shaded. The second solid line has a positive slope and goes through (0 comma negative 4) and (3 comma negative 2). Everything to the left of this line is shaded.
B
y is greater than negative 3 y is greater than or equal to 2 thirds x minus 4 Image with description On a coordinate plane, 2 straight lines are shown. The scale on both axes ranges from negative 5 to 5 in increments of 1. The first dashed line is parallel to the x-axis at y = negative 3. Everything above the dashed line is shaded. The second solid line has a positive slope and goes through (0 comma negative 4) and (3 comma negative 2). Everything to the left of this solid line is shaded.
C
y is less than negative 3 y is less than or equal to 2 thirds x minus 4 Image with description On a coordinate plane, 2 straight lines are shown. The scale on both axes ranges from negative 5 to 5 in increments of 1. The first dashed line is parallel to the x-axis at y = negative 3. Everything below the dashed line is shaded. The second solid line has a positive slope and goes through (0 comma negative 4) and (3 comma negative 2). Everything below the line is shaded.
D
y is greater than negative 2 y is less than or equal to 2 thirds x minus 4 Image with description On a coordinate plane, 2 straight lines are shown. The scale on both axes ranges from negative 5 to 5 in increments of 1. The first dashed line is parallel to the x-axis at y = negative 2. Everything above the dashed line is shaded. The second solid line has a positive slope and goes through (0 comma negative 4) and (3 comma negative 2). Everything to the right of this solid line is shaded.
7

Which graph shows the solution to the system of linear inequalities? y is less than or equal to 2 x minus 5 y is greater than negative 3 x plus 1

A
Image with description On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0 comma 1) and (1comma negative 2). Everything to the right of the line is shaded. The second dashed line has a positive slope and goes through (0 comma negative 5) and (2 comma negative 1). Everything to the right of the line is shaded.
B
Image with description On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0 comma 1) and (1 comma negative 2). Everything to the right of the line is shaded. The second solid line has a positive slope and goes through (0 comma negative 5) and (2 comma negative 1). Everything to the right of the line is shaded.
C
Image with description On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0 comma 1) and (1 comma negative 2). Everything to the left of the line is shaded. The second dashed line has a positive slope and goes through (0 comma negative 5) and (2 comma negative 1). Everything to the left of the line is shaded.
D
Image with description On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0 comma 1) and (1 comma negative 2). Everything to the left of the line is shaded. The second solid line has a positive slope and goes through (0 comma negative 5) and (2 comma negative 1). Everything to the left of the line is shaded.
8

Which graph shows the solution to the system of linear inequalities? x plus 3 y is greater than 6 y is greater than or equal to 2 x plus 4

A
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two straight lines on the graph. The first line is a dashed line that goes through the points (0 comma negative 2) and (3 comma negative 1). Everything below the dashed line is shaded. The second line is a solid line that goes through the points (2 comma 0) and (4 comma 4). Everything to the left of the solid line is shaded.
B
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two straight lines on the graph. The first line is a dashed line that goes through the points (0 comma negative 2) and (3 comma negative 1). Everything below the dashed line is shaded. The second line is a solid line that goes through the points (negative 2 comma 0) and (0 comma 4). Everything to the left of the solid line is shaded.
C
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two straight lines on the graph. The first line is a dashed line that goes through the points (0 comma 2) and (3 comma 1). Everything above the dashed line is shaded. The second line is a solid line that goes through the points (2 comma 0) and (4 comma 4). Everything to the left of the solid line is shaded.
D
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two straight lines on the graph. The first line is a dashed line that goes through the points (0 comma 2) and (3 comma 1). Everything above the dashed line is shaded. The second line is a solid line that goes through the points (negative 2 comma 0) and (0 comma 4). Everything to the left of the solid line is shaded.
9

Which graph shows the solution to the system of linear inequalities? x plus 5 y is greater than or equal to 5 y is less than or equal to 2 x plus 4

A
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two solid lines on the graph. The fist solid line goes through the points (0 comma 1) and (5 comma 0). Everything above the solid line is shaded. The second solid line goes through the points (negative 2 comma 0) and (negative 3 comma 2). Everything to the left of the solid line is shaded.
B
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two solid lines on the graph. The first solid line goes through the points (0 comma 1) and (5 comma 0). Everything above the solid line is shaded. The second solid line goes through the points (negative 2 comma 0) and (negative 1 comma negative 2). Everything to the left of the solid is shaded.
C
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two solid lines on the graph. The first solid line goes through the points (0 comma 1) and (5 comma 0). Everything above the solid line is shaded. The second solid line goes through the points (negative 2 comma 0) and (0 comma 4). Everything to the right of the solid line is shaded.
D
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two solid lines on the graph. The first solid line goes through the points (0 comma 1) and (5 comma 0). Everything above the solid line is shaded. A second solid line goes through the points (2 comma 0) and (0 comma 4). Everything to the left of the solid line is shaded.
10

Which graph shows the solution to the system of linear inequalities? y is greater than or equal to 2 thirds x plus 3 y is less than negative 1 third x plus 2

A
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two dashed straight lines on the graph. The first dashed line goes through the points (negative 3 comma 3) and (0 comma 2). Everything below the dashed line is shaded. The second dashed line goes through the points (negative 3 comma 1) and (3 comma 5). Everything to the left of the dashed line is shaded.
B
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. A dashed line goes through the point negative 1 comma 2.5 and the point 0 comma 3 and is shaded above the line. A second dashed line goes through the point negative 1 comma 2.5 and the point 0 comma 2 and is shaded above the line.
C
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. A dashed line goes through the point negative 1 comma 2.5 and the point 0 comma 3 and is shaded above the line. A solid line goes through the point negative 1 comma 2.5 and the point 0 comma 2 and is shaded below the line.
D
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. A dashed line goes through the point negative 1 comma 2.5 and the point 0 comma 3 and is shaded above the line. A solid line goes through the point negative 1 comma 2.5 and the point 0 comma 2 and is shaded above the line.

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