CA Foundation · Quantitative Aptitude · Linear Inequalities
The graph of the inequality 2x + 5y ≤ 20 is drawn, and the origin is tested. Which statement correctly describes the solution region?
The solution region is the half-plane containing the origin, including the boundary line. Putting (0,0) gives 0 ≤ 20, which is true, so the origin's side is the solution side. Because the sign is ≤ and not <, the line 2x + 5y = 20 belongs to the region.
- AThe half-plane containing the origin, including the line 2x + 5y = 20Correct
- BThe half-plane not containing the origin, including the line 2x + 5y = 20
- CThe half-plane containing the origin, excluding the line 2x + 5y = 20
- DThe half-plane not containing the origin, excluding the line 2x + 5y = 20
Explanation
At the origin, 2(0) + 5(0) = 0, and 0 ≤ 20 is true, so the origin lies in the solution region. The inequality is non-strict (≤), so points on the boundary line are included. Hence the region is the half-plane containing the origin together with the line.
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