Linear Inequalities in Two Variables · 6.2.2
Regions of inequality systems
Students test whether points lying in a region satisfy every inequality in a system simultaneously, then generalise that the region representing the system is the overlapping (intersection) region of all the individual inequality regions.
The official learning standard (6.2.2)
“Make and verify the conjecture about the points in the region and the solution of a system of linear inequalities.”
What it means
Students test whether points lying in a region satisfy every inequality in a system simultaneously, then generalise that the region representing the system is the overlapping (intersection) region of all the individual inequality regions.
How it is examined
Appears in Paper 1 as objective items asking whether a given point satisfies a system, and in Paper 2 where students verify specific points against a system of inequalities before sketching the combined region, usually as a lead-in to a shading question.
Worked example
Given the system y > x + 1 and x + y ≤ 6, determine whether the points (1, 4) and (5, 0) satisfy the system.
- Substitute (1, 4) into y > x + 1: 4 > 1 + 1 = 2, which is true.
- Substitute (1, 4) into x + y ≤ 6: 1 + 4 = 5 ≤ 6, which is true. So (1, 4) satisfies the system.
- Substitute (5, 0) into y > x + 1: 0 > 5 + 1 = 6, which is false.
- Since one inequality fails, (5, 0) does not satisfy the system.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What does it mean for a point to satisfy a system of inequalities?
It means the point's coordinates make every inequality in the system true at the same time, not just one of them.
How is this different from checking a single inequality?
For one inequality only that condition needs to be true; for a system, every listed inequality must be true at the same time for the point to be a valid solution.
What if a point lies exactly on a boundary line?
Check whether that inequality is strict (< or >) or inclusive (≤ or ≥); a boundary point only satisfies an inclusive inequality, not a strict one.