AnswersAlgebra ISolving Systems of Linear Inequalities

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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 1 comma negative 3
B
0 comma negative 1
C
negative 3 comma 5
D
negative 2 comma 2
2
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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 A coordinate plane with the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1, featuring 2 solid lines with shaded regions. The first solid line passes through the points, negative 4 comma 2, 0 comma 1, and 4 comma 0, with the region above the line shaded. The second solid line passes through the points, negative 5 comma 5, negative 2 comma 0 and negative 1 comma negative 2, with the region to the left of the line shaded. The two lines intersect between 2 and 3 on the x-axis and 1 and 2 on the y-axis. The region where both shades collide in the second quadrant is highlighted in a different shade.
B
Image with description A coordinate plane with the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1, featuring 2 solid lines with shaded regions. The first solid line passes through the points, negative 4 comma 2, 0 comma 1, and 4 comma 0, with the region above the line shaded. The second solid line passes through the points, negative 5 comma 5, negative 2 comma 0 and negative 1 comma negative 2, with the region to the left of the line shaded. The two lines intersect between 2 and 3 on the x-axis and 1 and 2 on the y-axis. The region where both shades collide in the second quadrant is highlighted in a different shade.
C
Image with description A coordinate plane with the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1, featuring 2 solid lines with shaded regions. The first solid line passes through the points negative 4 comma 2, 0 comma 1, and 4 comma 0, with the region above the line shaded. The second solid line passes through the points negative 1 comma 6, 0 comma 4, and 2 comma 0, with the region to the left of the line shaded. The two lines intersect between 1 and 2 on the x-axis and 0 and 1 on the y-axis. The region where both shades collide in the first and second quadrants is highlighted in a different shade.
D
Image with description A coordinate plane with the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1, featuring 2 solid lines with shaded regions. The first solid line passes through the points negative 4 comma 2, 0 comma 1, and 4 comma 0, with the region above the line shaded. The second solid line passes through the points negative 3 comma negative 2, negative 2 comma 0 and 0 comma 4, with the region to the right of the line shaded. The two lines intersect between negative 1 and negative 2 on the x-axis and 1 and 2 on the y-axis. The region where both shades collide in the first and second quadrants is highlighted in a different shade.
3

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 A coordinate plane with two lines and shaded regions. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 3 to 7 in increments of 1. A solid line with a positive slope intersects the y-axis at the point 0 comma 3. A dashed line with a negative slope intersects the y-axis at the point 0 comma 2. The region above both lines is shaded, the region below both lines is shaded, and the region above the solid line and below the dashed line is shaded.
B
Image with description A coordinate plane with two lines and shaded regions. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 3 to 7 in increments of 1. A solid line with a positive slope intersects the y-axis at the point 0 comma 3. A dashed line with a negative slope intersects the y-axis at the point 0 comma 2. The region above both lines is shaded, the region below the solid line and above the dashed line is shaded, and the region above the solid line and below the dashed line is shaded.
C
Image with description A coordinate plane with two lines and shaded regions. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 3 to 7 in increments of 1. A solid line with a positive slope intersects the y-axis at the point 0 comma 3. A dashed line with a negative slope intersects the y-axis at the point 0 comma 2. The region below both lines is shaded, the region below the solid line and above the dashed line is shaded, and the region above the solid line and below the dashed line is shaded.
D
Image with description A coordinate plane with two lines and shaded regions. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 3 to 7 in increments of 1. A solid line with a positive slope intersects the y-axis at the point 0 comma 3. A dashed line with a negative slope intersects the y-axis at the point 0 comma 2. The region above the solid line is shaded, the region below the solid line and above the dashed line is shaded, and the region below both lines is shaded.
4

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 A coordinate plane with two lines. The x-axis is labeled from negative 5 to 5, and the y-axis is labeled from negative 3 to 7. The first line is dashed, passes through the points 0 comma 2, and 6 comma 0, and has the region above it shaded. The second line is solid, passes through the points negative 2 comma 0, and 0 comma 4, and has the region above it shaded. The two shaded regions overlap in the upper left area of the graph.
B
Image with description A coordinate plane with two lines. The x-axis is labeled from negative 5 to 5 in increments of 1, and the y-axis is labeled from negative 3 to 7 in increments of 1. The first line is dashed, passes through the points 0 comma 2, and 3 comma 1, and has the region above it shaded. The second line is solid, passes through the points negative 2 comma 0, and 0 comma 4, and has the region above and to the left of it shaded. The two shaded regions overlap in the upper left area of the graph.
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 (negative 2 comma 0) and (0 comma 4). Everything to the left of the solid line is shaded.
D
Image with description A coordinate plane with two lines. The x-axis is labeled from negative 5 to 5, and the y-axis is labeled from negative 3 to 7. The first line is dashed, passes through the points 0, comma negative 2, and 3, comma negative 1, and has the region below it shaded. The second line is solid, passes through the points negative 2 comma 0, and 0 comma 4, and has the region to the left of it shaded. The two shaded regions overlap in the lower left area of the graph.
5

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

A
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.
B
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.
C
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.
D
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.
6

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 A coordinate plane with two lines and two shaded regions. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The letter y labels the vertical axis at the top and the letter x labels the horizontal axis at the right. A solid blue line with a positive slope passes through the origin and extends from the lower left to the upper right, reaching approximately negative 2 comma negative 4 at the lower end and 4 comma 5 at the upper end. A dashed red line with a steep negative slope passes through the upper portion of the left side of the plane, extending from approximately 0 comma 4 at the top downward to 2 comma negative 5 at the bottom. The region to the left of the dashed red line is shaded, covering the left side of the plane. A smaller triangular region near the lower right, bounded by the two lines and below the x-axis, is also shaded.
B
Image with description A coordinate plane with two lines. The x and y axes are labeled from negative 5 to 5 in increments of 1. The first line is dashed, passes through the points 0, comma 1, and 1 comma negative 2, and has the region below it shaded. The second line is solid, passes through the points 0, comma negative 5, and 2, comma negative 1, and has the region below it shaded. The two shaded regions overlap in the lower right area of the graph.
C
Image with description A coordinate plane with two lines. The x and y axes are labeled from negative 5 to 5 in increments of 1. The first line is dashed, passes through the points 0, comma 1, and 1 comma negative 2, and has the region below and to the right of it shaded. The second line is solid, passes through the points 0 comma negative 5 and 2, comma negative 1, and has the region below and to the right of it shaded. The two shaded regions overlap in the lower right area of the graph.
D
Image with description A coordinate plane with two lines. The x and y axes are labeled from negative 5 to 5 in increments of 1. The first line is dashed, passes through the points 0, comma 1, and 1 comma negative 2, and has the region below it shaded. The second line is solid, passes through the points 0 comma negative 5 and 2, comma negative 1, and has the region below it shaded. The two shaded regions overlap in the lower right area of the graph.
7

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 A coordinate plane with a horizontal x-axis and a vertical y-axis sits on a grid in increments of 1. The horizontal x-axis is labeled from negative 5 to 5. The vertical y-axis is labeled from negative 7 to 3. Two solid lines with arrowheads on both ends have a positive slope and run parallel to each other. The blue line passes through 0 comma 1 and negative 2 comma negative 3. The red line passes through 0 comma negative 2 and 1 comma 0. The region above the blue line is shaded blue, the region below the red line is shaded orange, and the region between the two lines is not shaded.
B
Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis sits on a grid in increments of 1. The horizontal x-axis is labeled from negative 5 to 5. The vertical y-axis is labeled from negative 7 to 3. Two lines with arrowheads on both ends have a positive slope and run parallel to each other. The blue line is solid and passes through 0 comma 1 and negative 2 comma negative 3. The red line is dashed and passes through 0 comma negative 2 and 1 comma 0. The region above the blue line is shaded blue, the region below the red line is shaded orange, and the region between the two lines is not shaded.
C
Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis sits on a grid in increments of 1. The horizontal x-axis is labeled from negative 5 to 5. The vertical y-axis is labeled from negative 7 to 3. Two solid lines with arrowheads on both ends have a positive slope and run parallel to each other. The blue line passes through 0 comma 1 and negative 2 comma negative 3. The red line passes through 0 comma negative 2 and 1 comma 0. The region to the left of the blue line is shaded orange, the region between the two lines is shaded purple, and the region to the right of the red line is shaded blue.
D
Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis sits on a grid in increments of 1. The horizontal x-axis is labeled from negative 5 to 5. The vertical y-axis is labeled from negative 7 to 3. Two lines with arrowheads on both ends have a positive slope and run parallel to each other. The blue line is solid and passes through 0 comma 1 and negative 2 comma negative 3. The red line is dashed and passes through 0 comma negative 2 and 1 comma 0. The region to the left of the blue line is shaded orange, the region between the two lines is shaded purple, and the region to the right of the red line is shaded blue.
8

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 A coordinate plane with two straight lines and two shaded regions. The x-axis and y-axis are each labeled from negative 5 to 5 in increments of 1. A solid straight line with a positive slope passes through the origin and extends from approximately the point negative 3 comma negative 3 to the point 3 comma 3, with an arrow at each end. A dashed straight line with a steeper positive slope also passes near the origin and extends from approximately the point negative 2 comma negative 5 to the point 2 comma 5, with an arrow at each end. The region between the two lines to the upper left is shaded, and the region outside both lines to the lower right is shaded, with the two shaded regions meeting near the origin.
B
Image with description A coordinate plane with two straight lines and two shaded regions. The x-axis and y-axis are each labeled from negative 5 to 5 in increments of 1. A solid straight line with a positive slope passes through the origin and extends from approximately the point negative 3 comma negative 3 to the point 3 comma 3, with an arrow at each end. A dashed straight line with a steeper positive slope also passes near the origin and extends from approximately the point negative 2 comma negative 5 to the point 2 comma 5, with an arrow at each end. The region above the dashed line to the upper left is shaded, and the region below the solid line to the lower right is shaded, with the two shaded regions not overlapping near the origin.
C
Image with description A coordinate plane with a parabola. The x-axis is labeled from negative 10 to 10 in increments of 2 and the y-axis is labeled from negative 10 to 10 in increments of 2. A parabola opens upward with its vertex at approximately the point 4 comma 0 on the x-axis, with the left side of the parabola rising steeply to approximately the point 2 comma 8 and the right side rising to approximately the point 6 comma 4, with arrows at both ends indicating the parabola continues beyond the top of the plane.
D
Image with description A coordinate plane with two straight lines and two shaded regions. The x-axis and y-axis are each labeled from negative 5 to 5 in increments of 1. A solid straight line with a positive slope passes through the origin and extends from approximately the point negative 3 comma negative 3 to the point 3 comma 3, with an arrow at each end. A dashed straight line with a steeper positive slope also passes near the origin and extends from approximately the point negative 2 comma negative 5 to the point 2 comma 5, with an arrow at each end. The region between the two lines to the lower right is shaded, and the region outside both lines to the upper left is shaded, with the two shaded regions meeting near the origin.
9

Which system of linear inequalities is represented by the graph?

A
y is less than or equal to x minus 2 and y is greater than or equal to x plus 1
B
y is greater than or equal to x minus 2 and y is less than or equal to x plus 1
C
y is greater than x minus 2 and y is less than x plus 1
D
y is less than x minus 2 and y is greater than x plus 1
10

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

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