AnswersNC-Math 2Solving Linear Systems by Substitution

Systems of Inequalities Answers

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Which point is a solution to the system of inequalities?

Question illustration
A
(–2, 6)
B
(1, 9)
C
(2, 8)
D
(0, 4)
2
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Which point is a solution to the system x2 + y2 ≤ 25 and x < y2 – 2?

A
(–5, 0)
B
(–2, 0)
C
(5, 0)
D
(2, 2)
3

One half the square of a number is less than a second number. The sum of 3 and the opposite of the second number is greater than the square of the first number.Which graph represents the solution set?

A
On a coordinate plane, a parabola opens up and goes through (negative 4, 8), has vertex (0, 0), and goes through (4, 8). Another parabola goes through (negative 3, negative 7), has vertex (0, 3), and goes through (3, negative 7). Everything outside of the first parabola and inside the second parabola is shaded.
Option A
B
On a coordinate plane, a parabola opens up and goes through (negative 4, 8), has vertex (0, 0), and goes through (4, 8). Another parabola goes through (negative 3, negative 7), has vertex (0, 3), and goes through (3, negative 7). Everything outside of both parabolas is shaded.
Option B
C
On a coordinate plane, a parabola opens up and goes through (negative 4, 8), has vertex (0, 0), and goes through (4, 8). Another parabola goes through (negative 3, negative 7), has vertex (0, 3), and goes through (3, negative 7). Everything inside of the first parabola and outside of the second parabola is shaded.
Option C
D
On a coordinate plane, a parabola opens up and goes through (negative 4, 8), has vertex (0, 0), and goes through (4, 8). Another parabola goes through (negative 3, negative 7), has vertex (0, 3), and goes through (3, negative 7). Everything inside the first parabola and inside the second parabola is shaded.
Option D
4

Which graph represents the solution of < 1 and y ≤?

Question illustration
A
On a coordinate plane, an ellipse has center (3, negative 2) and goes through (3, 0), (6, negative 2), (3, negative 4), and (0, negative 2). A curve starts at (1, negative 4) and goes up through (2, negative 3) and (11, negative 1). Everything inside of the ellipse and below the curve is shaded.
Option A
B
On a coordinate plane, an ellipse has center (3, negative 2) and goes through (3, 0), (6, negative 2), (3, negative 4), and (0, negative 2). A curve starts at (1, negative 4) and goes up through (2, negative 3) and (11, negative 1). Everything inside of the ellipse and above the curve is shaded.
Option B
C
On a coordinate plane, an ellipse has center (3, negative 2) and goes through (3, 1), (5.5, negative 2), (3, negative 5), and (0.5, negative 2). A curve starts at (1, negative 4) and goes up through (2, negative 3) and (11, negative 1). Everything inside of the ellipse and below the curve is shaded.
Option C
D
On a coordinate plane, an ellipse has center (3, negative 2) and goes through (3, 1), (5.5, negative 2), (3, negative 5), and (0.5, negative 2). A curve starts at (1, negative 4) and goes up through (2, negative 3) and (11, negative 1). Everything inside of the ellipse and above the curve is shaded.
Option D
5

Angela lives in a remote area serviced by only two cell phone towers. Tower 1 is located 5 miles west and 2 miles south of her home and transmits a signal for 12 miles. Tower 2 is located 8 miles east and 7 miles north of her home and transmits a signal for 10 miles. Consider the location of Angela’s house to be (0, 0) on a coordinate grid. The system of inequalities represents this scenario.

Question illustration
A
Angela will not have any cell phone service.
B
Angela will have cell phone service from tower 1 only.
C
Angela will have cell phone service from tower 2 only.
D
Angela will have cell phone service from both towers.
6

Review the graph.

Question illustration
A
36 > (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
B
36 > (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
C
36 (x – 4)2 + y2
D
36 (x – 4)2 + y2
7

Which graph represents the solution of x2 + 9y2 ≤ 81 and y2 + 2 < x?

A
On a coordinate plane, an ellipse has center (0, 0) and goes through (3, 0), (0, negative 9), (negative 3, 0), and (0, 9). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and outside of the parabola is shaded.
Option A
B
On a coordinate plane, an ellipse has center (0, 0) and goes through (3, 0), (0, negative 9), (negative 3, 0), and (0, 9). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and inside of the parabola is shaded.
Option B
C
On a coordinate plane, an ellipse has center (0, 0) and goes through (9, 0), (0, negative 3), (negative 9, 0) and (0, 3). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and inside of the parabola is shaded.
Option C
D
On a coordinate plane, an ellipse has center (0, 0) and goes through (9, 0), (0, negative 3), (negative 9, 0) and (0, 3). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and outside of the parabola is shaded.
Option D
8

Which graph represents the solution to the system of inequalities?

Question illustration
A
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases up through (0, 1) and (2, 4). A parabola opens to the right and goes through (9, 4), has vertex (4, 0), and goes through (9, negative 4). Another parabola opens to the left and goes through (negative 9, 4), has vertex (negative 4, 0), and goes through (negative 9, negative 4). Everything outside of the parabola and above the curve is shaded.
Option A
B
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases up through (0, 1) and (2, 4). A parabola opens to the right and goes through (9, 4), has vertex (4, 0), and goes through (9, negative 4). Another parabola opens to the left and goes through (negative 9, 4), has vertex (negative 4, 0), and goes through (negative 9, negative 4). Everything below the curve and inside both parabolas is shaded.
Option B
C
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases up through (0, 1) and (2, 4). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 2), (negative 4, 0), and (0, 2). Everything above the curve and inside of the ellipse is shaded.
Option C
D
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases up through (0, 1) and (2, 4). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 2), (negative 4, 0), and (0, 2). Everything below the curve and inside of the ellipse is shaded.
Option D
9

The sum of the squares of two different numbers is less than or equal to 49. Twice one of the numbers squared is less than the other number. Which system of inequalities represents these criteria?

A
x2 + y2 ≤ 49 and 2x2 < y
B
x2 + y2 ≥ 49 and 2x2 < y
C
x2 + y2 ≤ 49 and x2 < 2y
D
x2 + y2 ≥ 49 and x2 < 2y
10

A pair of fire towers uses technology to search for forest fires. Let the center of the forest be the origin on a coordinate grid. The first fire tower is located 5 km east and 8 km south of the center, and the second fire tower is located 7 km west and 4 km north of the center. The technology at the first tower can locate fires within a radius of 10 km and the second tower within a radius of 9 km. The system of inequalities represents this scenario.

Question illustration
A
2 km east and 3 km south
B
3 km east and 2 km north
C
2 km west and 1 km north
D
1 km west and 2 km south

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