Page 14 - Focus KSSM SPM 2021 TG4.5 - Maths DLP

Mathematics SPM Chapter 6 Linear Inequalities in Two Variables

D Solving problems involving systems The three linear inequalities that satisfy the
1
of linear inequalities in two variables shaded region are y  – x − 1, y  x + 2 and
2
x  2.
10
State the three inequalities that define the shaded 11
region in the diagram below. Write the three linear inequalities that satisfy the
(a) y given shaded region.
y 3
y

x 4
O
y 2x – 3 2 Form 4
x
–2 O 2 4
(b) y
Form 4
y x + 2
Solution
1 The shaded region is bounded by three straight lines.
y – x – 1
2
y
x
O
4
3
x 2 2 2
x
Solution –2 O 1 2 4
(a) The three straight lines involved are y = 3, x = 0
and y = 2x − 3. Equation of straight line 1
The shaded region is below the line y = 3 and is Straight line on the x-axis, thus y = 0
drawn with dashed line. The shaded region is above the line y = 0 and is drawn
Thus, y  3. with solid line. Thus, y  0.
The shade region is on the right of y-axis. Thus, Equation of straight line 2
x  0.
The shaded region is above the line y = 2x − 3 Gradient, m = 0 – 4 = 2
–2 – 0
and is drawn with solid line. y-intercept, c = 4
Thus, y  2x − 3. Thus, y = 2x + 4.
The three linear inequalities that satisfy the
shaded region are y  3, x  0 and y  2x − 3. The shaded region is below the line y = 2x + 4 and is
drawn with dashed line.
1 Thus, y  2x + 4.
(b) The three straight lines involved are y = – x − 1,
2
y = x + 2 and x = 2. Equation of straight line 3
1
The shaded region is above the line y = − x − 1 Gradient, m = 0 – 4 = −1
2
and is drawn with dashed line. 4 – 0
1
Thus, y  – x − 1. y-intercept, c = 4
2 Thus, y = −x + 4
The shaded region is below the line y = x + 2 and The shaded region is below the line y = −x + 4 and is
is drawn with solid line. drawn with solid line. Thus, y  −x + 4.
Thus, y  x + 2.
The shade region is on the left of line x = 2 The three linear inequalities that satisfy the shaded
and is drawn with solid line. Thus, x  2. region are y  0, y  2x + 4 and y  −x + 4.

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06 Focus SPM Maths F4.indd 94 17/02/2021 5:24 PM