Page 7 - Focus KSSM SPM 2021 TG4.5 - Maths DLP

Mathematics SPM Chapter 6 Linear Inequalities in Two Variables

Point A (–4, 0) Point B (2, 3) (c) For point (–6, –7)
y-coordinate y-coordinate y 2x + 5
p p
0  –4 – 1 3  2 – 1 –7 2(–6) + 5
q q –7 = –7
x-coordinate x-coordinate
y ∴ y = 2x + 5
4 Therefore, point (–6, –7) lies on the straight line
Half-plane B
y = x – 1 y = 2x + 5.
2
A x 3
–6 –4 –2 0 2 4 6 Determine whether each of the following point is the
–2 C Form 4
D solution for the linear inequalities given.
E Half-plane (a) (4, 5); y  –x + 2
Form 4
–4
(b) (–1, 2); y  3x – 4
(c) (–3, –7); 2x + y  –5
Point C (5, –2) Point D (0, –3) (d) (–3, 3); y  x + 6
y-coordinate y-coordinate
p p Solution
–2  5 – 1 –3  0 – 1
q q (a) y  -x + 2
x-coordinate x-coordinate
Left side Right side
3. Points that lie on the straight line, for example 5 –4 + 2
E(–3, –4) are the solutions for the straight line 5 -2
y = x – 1. 

2 Point satisfies
Determine whether each of the following point lies the inequality.
on the straight line, in the region above or below the Therefore, point (4, 5) is the solution of linear
straight line y = 2x + 5. inequality y  –x + 2.
(a) (–4, 2) (b) (1, 3)
(c) (–6, –7) (b)
y  3x – 4
Solution Left side Right side
(a) For point (–4, 2) 2 3(-1) – 4
y 2x + 5 2 -7
2 2(– 4) + 5 
2  -3
Point does not satisfy
∴ y  2x + 5 the inequality.
Therefore, point (–4, 2) lies in the region above Therefore, point (–1, 2) is not the solution of
the straight line y = 2x + 5. linear inequality y  3x – 4.
(b) For point (1, 3)
(c) 2x + y –5
y 2x + 5 
3 2(1) + 5 Left side Right side
3  7 2(-3) + (–7) –5
-13  –5
∴ y  2x + 5
Therefore, point (1, 3) lies in the region below the Therefore, point (–3, –7) is not the solution of
straight line y = 2x + 5. linear inequality 2x + y  –5.

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06 Focus SPM Maths F4.indd 87 17/02/2021 5:24 PM