Page 13 - Focus KSSM SPM 2021 TG4.5 - Maths DLP

Mathematics SPM Chapter 6 Linear Inequalities in Two Variables
1
8 (b) y  x, y  2x − 1 and y  −x + 6
2
Determine whether each of the following point y y 2x – 1
satisfies the inequalities y  –x + 3 and y  2x – 5.
(a) (–1, 2) y x
1
(b) (4, –3) 2
x
O
Solution y –x + 6
(a) Solution
True / True / (a)
Point y  –x + 3 y  2x – 5 • Mark the region that satisfies y  −x + 2 with
False False dots.
(–1, 2) 2  –(–1) + 3 True 2  2(–1) – 5 True • Mark the region that satisfies x  −1 with lines.
• Mark the region that satisfies y  0 with triangles. Form 4
Point (–1, 2) satisfies both inequalities y  –x + 3 • Shade the common region that marked with the
Form 4
and y  2x – 5. three markings.
(b) y
True / True /
Point y  –x + 3 y  2x – 5
False False
(4, –3) –3  –4 + 3 True –3  2(4) – 5 False x
O = 0 is x-axis.
Point (4, –3) does not satisfy both inequalities x –1 y –x + 2
y  –x + 3 and y  2x – 5.
Alternative method
y  −x + 2 ⇒ The region below the line
Try Question 2 in Try This! 6.2
y = −x + 2.
x  −1 ⇒ The region on the right of the line
C Determining and shading the region x = −1.
that satisfies a linear inequality y  0 ⇒ The region above the line y = 0.
system (b)
1
1. The region that satisfies a system of linear • Mark the region that satisfies y  x with A.
2
inequalities can be determined by the following • Mark the region that satisfies y  2x − 1 with B.
• Mark the region that satisfies y  –x + 6 with C.
steps: • Shade the common region that marked with the
(a) Mark the region of each linear inequality three letters.
with different marking.
(b) Identify the common region (intersection y y 2x – 1
of regions) of the markings. A
(c) Shade the common region completely. B A
1
C C A y x
2
9 A B B C B x
Shade the region that satisfies the given system of O y –x + 6
linear inequalities.
(a) y  −x + 2, x  −1 and y  0 Alternative method
1 1
y y  x ⇒ The region above the line y = x.
2 2
y  2x − 1 ⇒ The region below the line
y = 2x − 1.
y  −x + 6 ⇒ The region below the line
x y = −x + 6.
O
x –1 y –x + 2 Try Questions 3 – 5 in Try This! 6.2

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