iGCSE Mathematics (0580) :E2.6 Represent inequalities graphically and use this representation to solve simple linear programming problems.iGCSE Style Questions Paper 2

Question

Inequalities graph

The region R satisfies these three inequalities:

\( y > 1 \) \( y < 2x + 2 \) \( x + y \leq 3 \)

By drawing three suitable lines and shading unwanted regions, find and label the region R.

▶️ Answer/Explanation

Answer: The triangular region R is where all three conditions overlap (above \( y=1 \), below \( y=2x+2 \), and under \( x+y=3 \)).

Question

The graph of y = 2x + 1 is drawn on the grid.

By shading the unwanted regions of the grid, find and label the region R which satisfies these inequalities:

y ≥ 2x + 1 y ≥ 1 4x + 3y < 12

▶️ Answer/Explanation

Solution

Ans:

1. Draw y=2x+1 as solid line, shade above it

2. Draw y=1 as solid line, shade above it

3. Draw 4x+3y=12 as dashed line, shade below it

4. The region satisfying all three is the triangular area where all shadings overlap

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