MATHWITHCYE Relationship & Algebra

Linear Inequalities in Two Variables

Solid vs dashed boundary lines, identifying common feasible regions, and formulating mathematical models from word problems.

1

Boundary Line Conventions

The boundary line $y = mx + c$ divides the plane into two half-planes:

Solid Line (Garis Padu): For $\le$ or $\ge$. Points on the line are included in solution.
Dashed Line (Garis Sempang): For $<$ or $>$. Points on the line are NOT included.
2

The Origin Test Point $(0, 0)$

To determine which side of the line to shade:

Substitute $(0, 0)$ into inequality:
If TRUE $\implies$ shade the region containing $(0, 0)$.
If FALSE $\implies$ shade the opposite region!
3

Mathematical Modeling

Translating everyday constraints into inequalities:

  • "At most / tidak melebihi": $\le$
  • "At least / sekurang-kurangnya": $\ge$
  • "More than / lebih daripada": $>$
  • "Less than / kurang daripada": $<$

SPM Shading Traps: Clean Shading & Line Types

In SPM Paper 2, drawing a solid line when a dashed line was required automatically causes you to lose the boundary line mark! Ensure your pencil shading covers only the feasible region common to ALL stated inequalities.