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Quiz Chapter 6: Linear Inequalities in Two Variables

10 questions · Form 4 Mathematics Bab 6: Linear Inequalities in Two Variables

Question 1 of 10Score: 0

Identify the point that satisfies the system of inequalities: y ≤ x + 2 and y > -2x.

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. Identify the point that satisfies the system of inequalities: y ≤ x + 2 and y > -2x.

  1. A. (0, 3)
  2. B. (1, 1)
  3. C. (-2, 5)
  4. D. (0, -3)
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Answer: B

Test point (1, 1): 1 ≤ 1 + 2 = 3 (True) and 1 > -2(1) = -2 (True). Both inequalities are satisfied.

2. Which point satisfies the inequality 2x + y < 5?

  1. A. (2, 3)
  2. B. (1, 2)
  3. C. (3, 0)
  4. D. (2, 1)
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Answer: B

Substitute coordinates into 2x + y: For (1, 2): 2(1) + 2 = 4 < 5 (True). For (2, 1): 2(2) + 1 = 5, which is not strictly less than 5.

3. Consider the system: y > x, y < 4, x > 0. Which of the following points lies inside this feasible region?

  1. A. (1, 3)
  2. B. (3, 2)
  3. C. (2, 5)
  4. D. (-1, 2)
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Answer: A

Testing point (1, 3): 3 > 1 (True), 3 < 4 (True), 1 > 0 (True). All three conditions hold.

4. What type of line is drawn on a graph to represent the inequality y ≥ 2x + 1?

  1. A. Dashed line
  2. B. Solid line
  3. C. Dotted line
  4. D. Curved line
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Answer: B

Inequalities containing '≥' or '≤' include the points on the boundary line, so they are drawn with a solid line.

5. Does the origin (0, 0) satisfy the inequality 3x - 4y ≥ -12?

  1. A. Yes, because 0 ≥ -12 is True
  2. B. No, because 0 < -12 is False
  3. C. Only if x is negative
  4. D. Cannot be determined
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Answer: A

Substitute (0, 0): 3(0) - 4(0) = 0. Since 0 ≥ -12 is True, the origin satisfies the inequality.

6. Which of the following points lies in the solution set of y > 3x - 2?

  1. A. (1, 0)
  2. B. (2, 1)
  3. C. (0, 0)
  4. D. (3, 2)
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Answer: C

Substitute (0, 0): 0 > 3(0) - 2 ⇒ 0 > -2, which is a true statement.

7. Which inequality corresponds to the region to the right of the vertical line x = 3, excluding the line itself?

  1. A. x ≥ 3
  2. B. x > 3
  3. C. x ≤ 3
  4. D. x < 3
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Answer: B

Regions to the right of a vertical line correspond to greater values of x. Excluding the line requires the strictly greater symbol '>'.

8. Given the system x ≥ 0, y ≥ 0, x + y ≤ 6. What shape is formed by the solution region in the first quadrant?

  1. A. Circle
  2. B. Triangle
  3. C. Rectangle
  4. D. Hexagon
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Answer: B

The lines x = 0 (y-axis), y = 0 (x-axis), and x + y = 6 enclose a right-angled triangular region in the first quadrant.

9. If a point lies directly on a dashed boundary line of a shaded region, is it a solution to the inequality?

  1. A. Yes, always
  2. B. No, points on a dashed line are excluded from the solution region
  3. C. Only if x is positive
  4. D. Only if y is zero
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Answer: B

Points on a dashed line are excluded from the solution set because the inequality symbol is strict (< or >).

10. Which of the following is NOT a linear inequality in two variables?

  1. A. y - 2x ≥ 7
  2. B. x + y < 10
  3. C. 4x + y² > 1
  4. D. x2 + y3 ≤ 5
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Answer: C

Option C contains y², which makes it a non-linear inequality.

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