Page 12 - Focus KSSM SPM 2021 TG4.5 - Maths DLP

Mathematics SPM Chapter 6 Linear Inequalities in Two Variables

Linear (ii) Kim does not want to spend more than
Example of situation RM20 000 for the laptop inventory every
inequality
time.
y is at most k times x y  kx
Given the cost of laptop A is RM2 000 and laptop
Minimum of y is k y  k B is RM2 300.
Maximum of y is k y  k Solution
Sum of x and y is greater x + y  k (a) Let x represents the number of notebook and y
than k represents the number of drawing book.
Difference between y
and x is less than k y – x  k First inequality:
3x + 7y  30 Spend not more than the
Sum of x and y is at most x + y  k voucher value of RM30.
k Form 4
Second inequality:
y is more than x by at y – x  k x  y Number of notebook purchased is less
Form 4
least k than drawing book.

7 (b) Let x represents the number of bottles for
Represent each of the following situation in the form pineapple jam and y represents the number of
bottles for strawberry jam.
of system of linear inequalities.
(a) Alia has a RM30 voucher that can be used at 3x + 11 y  11 First inequality:
Total operation time for cooking
a stationery store. A notebook and a drawing 4 process.
book cost RM3 and RM7 respectively. Alia plans
5
to spend not more than the voucher value. The 5 x + y  8 Second inequality:
Total operation time for
number of notebooks to be purchased is less 4 6 cooling process.
than the number of drawing books.
(b) A factory produces pineapple and strawberry (c) Let x represents the number of laptop A and y
jam. The table shows the process and time used represents the number of laptop B.
to produce the jam.
x  2y First inequality:
Pineapple Strawberry The number of laptop A is at most
Process 2 times the number of laptop B.
jam jam
2 000x + 2 300y  20 000
3
Cooking (hour) 3 2 4 Second inequality: Inventory of laptop A
and laptop B is not more than RM20 000.
1 5
Cooling (hour) 1 4 6
Try Question 1 in Try This! 6.2
The cooking and cooling section operate for 11
hours and 8 hours daily respectively. In a day, the
factory is able to produce x bottles of pineapple B Verifying the conjecture about the
jam and y bottles of strawberry jam. points in the region and the solution
(c) Kim sells two types of laptop in his shop. He of linear inequalities system
needs to make inventory for the laptops every
month. The following is his consideration when 1. Points that satisfy all linear inequalities lie
preparing the inventory. in the common region of the inequalities.
(i) Inventory of laptop A is at most two times Therefore, the points are known as the solutions
the inventory of laptop B. of the system of linear inequalities.

92

06 Focus SPM Maths F4.indd 92 17/02/2021 5:24 PM