Systems of Inequalities

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10.4Systems of Inequalities

Systems of Inequalities Revision Questions

1. . The system of linear inequalities

x - 2 < 3y2x - y > 1

is equivalent to

  1. y - 2 < 3x2x > 1 + y
  2. y < x/3 - 2/3y > 2x - 1
  3. y < x/3 - 2/3y > 2x - 1
  4. y > x/3 - 2/3y < 2x - 1

Correct Answer: D

2. . The solution set of the system of linear inequalities

x - 1 > yy + 3x < 2

lies

  1. Above the intercept
  2. Below the intercept
  3. On the left of the intercept
  4. On the right of the intercept

Correct Answer: B

3. . The solution set of the system of linear inequalities

2x - y > 3x + y > -2

lies

  1. Above the intercept
  2. Below the intercept
  3. On the left of the intercept
  4. On the right of the intercept

Correct Answer: D

4. . What are the coordinates of the maximum point for the solution set in the system of inequalities

x - 4 ≥ yy ≤ 2x + 1
  1. (-1, -3)
  2. (-2, -6)
  3. Infinity
  4. (0, 0)

Correct Answer: C

5. . What is the minimum point of the solution set for the system of linear inequalities

3x - 1 < y2x + y > 5
  1. (6/5, 13/5)
  2. (13/5, 6/5)
  3. (0, 0)
  4. (1, 6/5)

Correct Answer: A

6. . What is the system of linear inequalities shown in the figure?

Math Tutorials: Systems of Inequalities Example
  1. y > x - 1y ≤ 4x
  2. y ≥ x - 1y ≤ 4x
  3. y > 2x - 1y ≤ 4x
  4. y ≥ x - 1y < 4x

Correct Answer: B

7. . What are the coordinates of the maximum point of the solution set for the system of linear inequalities

y < 2 - xy>3x + 1x > -2
  1. (1, 3/4)
  2. (3/4, 1)
  3. (1/4, 7/4)
  4. (7/4, 1/4)

Correct Answer: C

8. . What are the coordinates of the minimum point of the solution set for the system of inequalities

x ≥ 0x ≤ 42x - y ≤ 3
  1. (4, 5)
  2. (0, 0)
  3. (0, -3)
  4. (4, 0)

Correct Answer: C

9. . Which part of the graph below shows the solution set of the system of inequalities

y ≥ 2x - 3y≥x2 - 4x + 1
Math Tutorials: Systems of Inequalities Example
  1. Zone 1
  2. Zone 2
  3. Zone 3
  4. Zone 4

Correct Answer: B

10. . The solution set of the system of inequalities

y (?1) 3x + 1y (?2) - x + 5

lies in zone 3 of the graph below. What are the inequality symbols (?1) and (?2)?

Math Tutorials: Systems of Inequalities Example
  1. (?1) is "≥" and (?2) is "≥"
  2. (?1) is "≥" and (?2) is "≤"
  3. (?1) is "≤" and (?2) is "≥"
  4. (?1) is "≤" and (?2) is "≤"

Correct Answer: C

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