AnswersAPSB 2025 Math Essentials-ALPGraphing Two-Variable Linear Inequalities

Solving Systems of Linear Inequalities Answers

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1
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Which system of inequalities with a solution point is represented by the graph?

A
y > 2x – 2 and y < x – 1; (3, 1)
B
y > 2x – 2 and y < x + 1; (–3, 1)
C
y > 2x + 2 and y < x – 1; (3, 1)
D
y > 2x + 2 and y < x + 1; (–3, 1)
2
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A
(–4, –2)
B
(–1, –2)
C
(1, 4)
D
(2, 2)
3

y > 2x +2y > –2x – 1y < 2x + 2y < –2x – 1

A
y > 2x +2
B
y > –2x – 1
C
y < 2x + 2
D
y < –2x – 1
4

Which statements are true about the graph of y ≤ 3x + 1 and y ≥ –x + 2? Check all that apply.The slope of one boundary line is 2.Both boundary lines are solid.A solution to the system is (1, 3).Both inequalities are shaded below the boundary lines.The boundary lines intersect.

A
The slope of one boundary line is 2.
B
Both boundary lines are solid.
C
A solution to the system is (1, 3).
D
Both inequalities are shaded below the boundary lines.
E
The boundary lines intersect.
6

Which ordered pairs make both inequalities true? Check all that apply.

A
(–2, 2)
B
(0, 0)
C
(1,1)
D
(1, 3)
E
(2, 2)
7

Graphically, a point is a solution to a system of two inequalities if and only if the point

A
lies in the shaded region of the top inequality, but not in the shaded region of the bottom inequality.
B
lies in the shaded region of the bottom inequality, but not in the shaded region of the top inequality.
C
lies in the shaded regions of both the top and bottom inequalities.
D
does not lie in the shaded region of the top or bottom inequalities.
9

Which is the graph of the system x + 3y > –3 and y < x + 1?

Question illustration
A
[Image: On a coordinate plane, 2 dashed lines are shown. T...]
Option A
B
[Image: On a coordinate plane, 2 dashed lines are shown. T...]
Option B
C
[Image: On a coordinate plane, 2 dashed lines are shown. T...]
Option C
D
[Image: On a coordinate plane, 2 dashed lines are shown. T...]
Option D
10

Which statements are true about the graph of y ≤ 3x + 1 and y ≥ –x + 2? Check all that apply.The slope of one boundary line is 2.Both boundary lines are solid.A solution to the system is (1, 3).Both inequalities are shaded below the boundary lines.The boundary lines intersect.

A
The slope of one boundary line is 2.
B
Both boundary lines are solid.
C
A solution to the system is (1, 3).
D
Both inequalities are shaded below the boundary lines.
E
The boundary lines intersect.
11

(–4, –2)✔ (–1, –2)X (1, 4)(2, 2)

A
(–4, –2)
B
✔ (–1, –2)
C
X (1, 4)
D
(2, 2)

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