Linear Inequalities in Two Variables · 6.2.1
Representing systems of inequalities
Pupils translate a real-life situation involving two or more conditions, such as a budget and a minimum quantity, into two or more linear inequalities in two variables that must all be true at the same time, forming a system of linear inequalities representing the situation completely.
The official learning standard (6.2.1)
“Represent situations in the form of a system of linear inequalities.”
What it means
Pupils translate a real-life situation involving two or more conditions, such as a budget and a minimum quantity, into two or more linear inequalities in two variables that must all be true at the same time, forming a system of linear inequalities representing the situation completely.
How it is examined
Paper 2 structured questions commonly describe a real situation with several restrictions and require pupils to represent it as a system of linear inequalities, usually including non-negative conditions on x and y, before using the system to shade a region and solve further parts of the question.
Worked example
A stall sells key chains at RM3 each and stickers at RM1 each. A customer buys x key chains and y stickers such that the total cost does not exceed RM24, and the total number of items bought is at least 10.
Write the system of linear inequalities representing this situation, given that x ≥ 0 and y ≥ 0.
- Cost condition: x key chains cost 3x, y stickers cost y, total cost ≤ 24, so 3x + y ≤ 24.
- Quantity condition: total items at least 10, so x + y ≥ 10.
- Since x and y are numbers of items, they cannot be negative: x ≥ 0, y ≥ 0.
- Combine all four conditions into one system.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How many inequalities can a system have?
A system can have two or more linear inequalities, one for each condition or restriction described in the situation, plus any non-negativity conditions, such as x ≥ 0 and y ≥ 0, where the variables represent quantities that cannot be negative.
Why are x ≥ 0 and y ≥ 0 often included?
These conditions are included when x and y represent real-world quantities that cannot be negative, such as numbers of items bought or produced, so they help define a realistic solution region alongside the other inequalities in the system.
What is the difference between a single inequality and a system?
A single inequality represents one condition relating x and y. A system combines two or more inequalities that must all be true at the same time, representing several conditions from the same situation together as a complete set of requirements.