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Linear Equations and Inequalities MCQs — Mathematics (page 2)

45 multiple-choice questions on Linear Equations and Inequalities from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.

26. Pens cost Rs. 20 and notebooks Rs. 50. A student has at most Rs. 300 and wants at least 2 notebooks. With x pens and y notebooks, the conditions are:

  1. 20x + 50y ge 300, y ge 2
  2. 20x + 50y le 300, y le 2
  3. 50x + 20y le 300, x ge 2
  4. 20x + 50y le 300, y ge 2

Answer: D) 20x + 50y le 300, y ge 2

Explanation: Total cost cannot exceed 300 (le), and the number of notebooks is at least 2 (y ge 2). SLO M-10-A-23 · Understanding

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27. Which region satisfies x 0 and y < 0?

  1. Quadrant IV
  2. Quadrant III
  3. Quadrant II
  4. Quadrant I

Answer: A) Quadrant IV

Explanation: Positive x and negative y is quadrant IV. SLO M-10-A-23 · Understanding

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28. A farmer has 10 acres for wheat (x) and cotton (y) and must plant at least 3 acres of wheat. Which pair of inequalities describes this (with y ge 0)?

  1. x + y le 10, x ge 3
  2. x - y le 10, y ge 3
  3. x + y ge 10, x ge 3
  4. x + y le 10, x le 3

Answer: A) x + y le 10, x ge 3

Explanation: Total land is at most 10 acres; wheat is at least 3 acres. SLO M-10-A-23 · Understanding

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29. Which point is not in the solution region of x + y le 6 and x - y ge 2?

  1. (0, -3)
  2. (5, 0)
  3. (2, 2)
  4. (2, -3)

Answer: C) (2, 2)

Explanation: (2, 2) fails at least one of the inequalities; the other points satisfy both. SLO M-10-A-23 · Understanding

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30. The boundary lines x + 2y = 7 and 3x - y = 7 meet at the corner point:

  1. (-3, 2)
  2. (2, 3)
  3. (3, 2)
  4. (4, 1)

Answer: C) (3, 2)

Explanation: Solving the two equations together gives x = 3, y = 2. SLO M-10-A-23 · Understanding

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31. Solve 25x + 34 = - 920.

  1. x = 3
  2. x = - 98
  3. x = -3
  4. x = 34

Answer: C) x = -3

Explanation: 25x = - 920 - 34 = - 65, so x = - 65 div 25 = -3. SLO M-09-A-22 · Understanding

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32. Solve 3x - 4 ge 8.

  1. x ge 4
  2. x ge -4
  3. x le 4
  4. x le -4

Answer: A) x ge 4

Explanation: 3x ge 12. Dividing by 3 keeps the sign: x ge 4. SLO M-09-A-22 · Understanding

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33. A number line shows a closed (filled) circle at -2 and an arrow pointing right. Which inequality does it represent?

  1. x le -2
  2. x ge -2
  3. x < -2
  4. x -2

Answer: B) x ge -2

Explanation: An open circle means the end point is not included (< or ); a closed circle means it is included (le or ge). SLO M-09-A-22 · Understanding

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34. Solve 13x + 12 = 76.

  1. x = 2
  2. x = 72
  3. x = -2
  4. x = 5

Answer: A) x = 2

Explanation: 13x = 76 - 12 = 23, so x = 23 div 13 = 2. SLO M-09-A-22 · Understanding

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35. The boundary lines x + y = 6 and x - y = 2 meet at the corner point:

  1. (2, 4)
  2. (5, 1)
  3. (-4, 2)
  4. (4, 2)

Answer: D) (4, 2)

Explanation: Solving the two equations together gives x = 4, y = 2. SLO M-10-A-23 · Understanding

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36. On a number line, the solution of x 5 is shown by:

  1. an open circle at 5 with an arrow to the right
  2. an open circle at 5 with an arrow to the left
  3. a closed circle at 5 with an arrow to the right
  4. a closed circle at 5 with an arrow to the left

Answer: A) an open circle at 5 with an arrow to the right

Explanation: 5 itself is not included (open circle), and all larger numbers are (arrow to the right). SLO M-09-A-22 · Understanding

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37. Solve 2x + 15 x - 22.

  1. x < -12
  2. x 12
  3. x < 12
  4. x < 8

Answer: C) x < 12

Explanation: Multiply by 10: 2(2x + 1) 5(x - 2) Rightarrow 4x + 2 5x - 10 Rightarrow 12 x. SLO M-09-A-22 · Understanding

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38. When graphing y < 2x + 1, the boundary line is drawn:

  1. dashed, and the region below it is shaded
  2. solid, and the region below it is shaded
  3. dashed, and the region above it is shaded
  4. solid, and the region above it is shaded

Answer: A) dashed, and the region below it is shaded

Explanation: A strict inequality (<) uses a dashed line; y < means the region below the line. SLO M-10-A-23 · Understanding

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39. Solve -3x - 1 8.

  1. x -3
  2. x < 3
  3. x 3
  4. x < -3

Answer: D) x < -3

Explanation: -3x 9. Dividing by -3 reverses the sign because it is negative: x < -3. SLO M-09-A-22 · Understanding

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40. Which point satisfies both x + y le 6 and x - y ge 2?

  1. (6, 0)
  2. (-2, -3)
  3. (1, 0)
  4. (-3, -1)

Answer: A) (6, 0)

Explanation: Substitute (6, 0): it makes both inequalities true. Each other point fails at least one of them. SLO M-10-A-23 · Understanding

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41. The inequality 2x - y 4 can be rewritten as:

  1. y < 2x - 4
  2. y < 4 - 2x
  3. y 2x - 4
  4. y 2x + 4

Answer: A) y < 2x - 4

Explanation: -y 4 - 2x; multiplying by -1 reverses the sign: y < 2x - 4. SLO M-10-A-23 · Understanding

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42. Ali's age in 5 years will be 32 of his age 5 years ago. His present age is:

  1. 25 years
  2. 20 years
  3. 15 years
  4. 30 years

Answer: A) 25 years

Explanation: x + 5 = 32(x - 5) Rightarrow 2x + 10 = 3x - 15 Rightarrow x = 25. SLO M-09-A-22 · Understanding

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43. Which point satisfies both 3x + 2y le 12 and x ge 1?

  1. (-2, -3)
  2. (5, 6)
  3. (-2, 0)
  4. (1, -3)

Answer: D) (1, -3)

Explanation: Substitute (1, -3): it makes both inequalities true. Each other point fails at least one of them. SLO M-10-A-23 · Understanding

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44. A number line shows an open circle at 3 and an arrow pointing left. Which inequality does it represent?

  1. x 3
  2. x le 3
  3. x < 3
  4. x ge 3

Answer: C) x < 3

Explanation: An open circle means the end point is not included (< or ); a closed circle means it is included (le or ge). SLO M-09-A-22 · Understanding

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45. Which point satisfies both x + 2y ge 4 and x - y < 1?

  1. (3, -3)
  2. (6, -2)
  3. (1, -3)
  4. (-1, 4)

Answer: D) (-1, 4)

Explanation: Substitute (-1, 4): it makes both inequalities true. Each other point fails at least one of them. SLO M-10-A-23 · Understanding

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