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GCE Mathematics 1990 Question 17

Question 17

Inequalities

The area shaded with vertical lines is the solution set of the inequalities:

Diagram for this question
  1. A.y ≤ x, y + 2x ≤ −3
  2. B.y ≥ x, y + 2x ≥ −3
  3. C.y ≤ x, y ≤ 2x − 3, x ≤ 3
  4. D.y ≤ −x, y ≤ 2x − 3, x ≤ 3
  5. E.y ≥ x, y + 2x ≥ 3, x ≤ 3
Show the answer and explanation

Answer: A (y ≤ x, y + 2x ≤ −3)

Explanation

The vertical-lined region lies below the line y = x and below the falling line y + 2x = −3, so y ≤ x and y + 2x ≤ −3.