Linear Inequalities in Two Variables · Form 4
Linear Inequalities in Two Variables: Key Terms
The key Linear Inequalities in Two Variables terms you need for SPM Mathematics, defined plainly in English, Malay and Chinese.
- Linear inequality A relationship like y ≥ 2x + 1 that describes a region of the graph rather than a single line.
- Feasible region The region of a graph that satisfies all the given inequalities at once.
- Inequality A statement that one quantity is greater than or less than another, using <, >, ≤ or ≥.
- Number line A line on which numbers are marked at equal intervals, used to show the solution of an inequality.
- y-intercept The point where a graph crosses the y-axis.
Term pairs students confuse
- Linear inequality vs linear equation, an equation (y = 2x + 1) is a single line; an inequality (y ≥ 2x + 1) is a whole region on one side of that line.
- Solid line vs dashed line, solid means the boundary is included (≤, ≥); dashed means it is excluded (<, >).
- Feasible region vs boundary line, the boundary is the edge you rule; the feasible region is the area, usually labelled R, that satisfies every inequality at once.
- 'At least' vs 'at most' 'at least k' means ≥ k (k and above); 'at most k' means ≤ k (k and below); they shade opposite sides.
- x-intercept vs y-intercept, the x-intercept is where a line crosses the x-axis (set y = 0); the y-intercept is where it crosses the y-axis (set x = 0); you need both to plot a boundary accurately.
How these terms are phrased inside real SPM questions
In Paper 2 the constraints rarely arrive as ready-made symbols. You will read phrases such as 'the number of chairs is at most 40' (x ≤ 40), 'the number of tables is not more than twice the number of chairs' (x ≤ 2y), or 'at least RM50 is spent' (≥ 50).
The command words are exact too: 'write three inequalities' means you form them yourself; 'shade the region R that satisfies all the inequalities' means the overlap of every shading, not any one alone; and 'hence find the maximum value' expects you to test the corners of that region. Before translating, underline every 'at least', 'at most', 'not exceeding', 'minimum' and 'maximum' each one fixes a direction, and a single misread word turns the whole region inside out.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Is the 'feasible region' the same thing as the 'solution' of the inequalities?
Yes, they describe the same thing. A single linear inequality in two variables has infinitely many solutions, and together they form a region, not a list of numbers.
The feasible region is exactly the set of all points (x, y) that satisfy every inequality at once, so shading it is how you present the solution on a graph.
What does 'satisfies the inequality' actually mean when I test a point?
It means substituting the point's x and y into the inequality gives a true statement. For y ≥ 2x with the point (3, 4), you get 4 ≥ 6, which is false, so (3, 4) does not satisfy it and lies outside that region.
A point satisfies a set of inequalities only if it makes every one of them true.
Why is it called a linear inequality in TWO variables?
Because two unknowns, usually x and y, appear together, so each solution is a pair of values plotted as a point on the plane. That is why the answer is a two-dimensional region rather than a stretch of the number line, which is what a one-variable inequality like x > 3 gives.
'Linear' means x and y appear only to the first power, so every boundary is a straight line.