Page 60 - Hybrid PBD 2022 Form 4 Additional Mathematics

Matematik Tambahan Tingkatan 4 Bab 3 Sistem Persamaan
3. Selesaikan persamaan serentak berikut. 4. Rajah di bawah menunjukkan kolam ikan ABCD
Solve the following simultaneous equations. yang dikelilingi papan kayu sebagai laluan di
x(7y + x) = 16 − 34y 2 sebuah kelong ikan. KBAT Mengaplikasi
2x − 14y = 4 The diagram below shows a fish pond ABCD surrounded by
[5 markah / 5 marks] wooden boards as pathway in a fish kelong.
Jawapan / Answer : 2(y – 1) m
x(7y + x) = 16 − 34y 2 P Q
7xy + x + 34y = 16 ....................... A y m B
2
2
2x − 14y = 4 Kolam ikan x m 3x – m
7
2x = 14y + 4 Fish pond 2
x = 7y + 2 ............................b D C
Gantikan b ke dalam  S R
Penerbitan Pelangi Sdn Bhd. All Rights Reserved
Substitute b into 
7y(7y + 2) + (7y + 2) + 34y = 16 Diberi bahawa perimeter kolam ikan ABCD ialah
2
2
2
49y + 14y + 49y + 28y + 4 + 34y − 16 = 0 16 m dan luas papan kayu ialah 29 m . Cari luas,
2
2
2
2
2
132y + 42y − 12 = 0 dalam m , kolam ikan ABCD jika y  x.
Given that the perimeter of the fish pond ABCD is 16 m and the
22y + 7y − 2 = 0 area of the wooden boards is 29 m . Find the area, in m , of the
2
2
2
(11y − 2)(2y + 1) = 0 fish pond ABCD if y  x.
y = 2 , y = − 1 [5 markah / 5 marks]
11 2
KBAT
Apabila / When y = 2 Tip KBATKBAT
11 Luas papan kayu = luas PQRS – luas ABCD
2
x = 7   + 2 Area of the wooded board = area of PQRS – area of ABCD
11
36
= Jawapan / Answer :
11 2x + 2y = 16
Apabila / When y = − 1 x + y = 8 ............................................
2 7

1
 
x = 7 − + 2 2(y − 1) 3x − 2  − xy = 29 ................b
2
= − 3 Dari  / From : y = 8 − x ................c
2
Gantikan c ke dalam b
3
∴ x = 36 , y = 2 dan / and x = − , y = − 1 Substitute c into b
11 11 2 2 2(8 − x − 1) 3x − 7  − x(8 − x) = 29

2
7


2 21x − 49 − 3x + x − 8x + x − 29 = 0
2
2
2
2

2
2
2 –3x + 49 x – 49  − 8x + x − 29 = 0
2
2
2
−5x + 41x − 78 = 0
2
−41 ±  − 4(−5)(−78)
41
x =
2 (−5)
x = 3 atau / or x = 5.2
Apabila / When x = 3
y = 8 − 3
= 5
Apabila / When x = 5.2
y = 8 − 5.2
= 2.8
Maka, / Thus, x = 3, y = 5
Luas kolam ikan ABCD / Area of the fish pond ABCD
= 3 × 5
= 15 m 2
© Penerbitan Pelangi Sdn. Bhd. 42

03 Hybrid PBD Mate Tambahan Tg4.indd 42 29/09/2021 3:30 PM