Linear Inequalities in Two Variables · Form 4
Why an inequality gives you a region, not a line
An equation like y = x + 1 is satisfied only by the points sitting exactly on one line; an inequality like y ≥ x + 1 is satisfied by every point on a whole side of that line, so its solution is a region of the plane.
From one line to a whole side
The equation y = x + 1 draws a single straight line, and every point on it makes the two sides equal. Swap the = for ≥ and you now accept every point where y is at least x + 1, which fills the entire region on one side of the line.
The line itself is just the boundary; the real answer is the shaded area beside it, not the line alone.
Recognising it by the sign
You can tell which you have from the symbol: an = sign means an equation and gives a line, while <, >, ≤ and ≥ mean an inequality and give a region. The boundary is drawn solid for ≤ or ≥ because points on the line count, and dashed for < or > because points on the line are excluded.
Reading the sign tells you both which side belongs and whether the edge itself is included.
The usual misconception
Students often shade only the line itself, or a thin strip beside it, or assume that 'above the line' always means ≥. In fact the region is unbounded, stretching out without end on one side, and which side to shade depends on the actual inequality rather than on where the line appears to sit.
Substituting a test point such as (0, 0) into the inequality tells you which side is correct.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Why is the boundary line sometimes solid and sometimes dashed?
A solid line means the boundary itself is included, used for ≤ or ≥, because points on the line also satisfy the inequality. A dashed line means the boundary is excluded, used for strict < or >.
In Paper 2, check the inequality sign before drawing, since examiners check this detail carefully.
How do I decide which side of the line to shade?
Pick any point not on the line, usually the origin (0, 0) if it isn't on the line, and substitute it into the inequality. If the point satisfies the inequality, shade the side containing it; if not, shade the opposite side.
This test-point method avoids guessing from the inequality sign alone.
What mistake costs marks when shading the region?
A common mistake is shading both sides or forgetting to shade at all, and leaving the region unlabelled. Examiners expect the required region marked clearly, often with the letter R, so unlabelled or ambiguous shading loses marks even if the boundary line is correct.