4MA1/1H Jan 2023, Question 11: Finding Regions from Multiple Inequalities
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 3 marks
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The question, in short
From a diagram showing region R bounded by 2x + y = 6, 2y = 5x + 1 and 3y + 2x = 4, write the three inequalities defining R.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1Identify the boundary lines: 2x + y = 6, 2y = 5x + 1, 3y + 2x = 4
- 2Determine the inequality direction for each line based on the shaded region R
- 3For 2x + y = 6, the region is below the line, so 2x + y ≤ 6
- 4For 2y = 5x + 1, the region is below the line, so 2y ≤ 5x + 1
- 5For 3y + 2x = 4, the region is above the line, so 3y + 2x ≥ 4
- 62x + y ≤ 6, 2y ≤ 5x + 1, 3y + 2x ≥ 4
Answer2x + y ≤ 6, 2y ≤ 5x + 1, 3y + 2x ≥ 4
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