Linear Inequalities in Two Variables · 6.2.4
Solving inequality system problems
Students translate a real-world scenario with two or more constraints into a system of linear inequalities, sketch and shade the region representing all the constraints together, then use the graph to identify combinations of quantities that satisfy every condition.
The official learning standard (6.2.4)
“Solve problems involving systems of linear inequalities in two variables.”
What it means
Students translate a real-world scenario with two or more constraints into a system of linear inequalities, sketch and shade the region representing all the constraints together, then use the graph to identify combinations of quantities that satisfy every condition.
How it is examined
Appears mainly in Paper 2 as an extended structured question: forming inequalities from a word problem, shading the solution region, then identifying or verifying specific integer solutions (such as possible quantities of two items) that satisfy the whole system.
Worked example
A shop sells chairs (x units) and tables (y units). Stock allows x + y ≤ 10, and demand requires y ≥ x − 2, with x ≥ 0 and y ≥ 0.
State one possible combination of (x, y) and show that it satisfies all the constraints.
- List the constraints: x + y ≤ 10, y ≥ x − 2, x ≥ 0, y ≥ 0.
- Try (x, y) = (4, 4): x + y = 4 + 4 = 8 ≤ 10, which is true.
- Check y ≥ x − 2: 4 ≥ 4 − 2 = 2, which is true; also x ≥ 0 and y ≥ 0 are both true.
- All four inequalities are satisfied by (4, 4).
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I turn a word problem into inequalities?
Identify each limiting phrase (at most, no more than, at least, minimum) and translate it directly into ≤ or ≥ using the given variables, keeping units consistent throughout the problem.
Do I need to shade the graph for every problem?
Most Paper 2 questions of this type require a sketch with the region shaded, since that is usually how marks are awarded for correctly identifying valid solutions.
Can the answer be any point in the shaded region?
Only if the problem allows non-integer values; many real-life contexts (like a number of chairs) require whole-number points within or on the boundary of the shaded region.