Page 45 - Steady Mate Tg1 - Book B

Matematik Tingkatan 1 Bab 6 Persamaan Linear

K Selesaikan setiap persamaan linear serentak yang berikut dengan menggunakan kaedah penggantian. TP 3 ARAS R
Solve each of the following simultaneous linear equations by using substitution method.

Contoh 1. x + 2y = 6 ........................................ a
4x + 3y = 9 ...................................... b
2x + y = 5. ...................................... a
2x + 3y = 7 ................................... b Daripada / From a, x = 6 – 2y ....... c
Daripada / From a, y = 5 – 2x .... c Gantikan c ke dalam b.
Substitute c into b.
Gantikan c ke dalam b. 4(6 – 2y) + 3y = 9
Substitute c into b. 24 – 8y + 3y = 9
2x + 3(5 – 2x) = 7 24 – 5y = 9
2x + 15 – 6x = 7 –5y = 9 – 24
15 – 4x = 7 –5y = –15
– 4x = 7 – 15 y = 3
– 4x = – 8
x = 2
Gantikan y = 3 ke dalam c.
Gantikan x = 2 ke dalam c. Substitute y = 3 into c.
Substitute x = 2 into c. x = 6 – 2(3)
y = 5 – 2(2) = 6 – 6
= 5 – 4 = 0
= 1
Maka / Thus, x = 0 dan / and y = 3.
Maka / Thus, x = 2 dan / and y = 1.

2. 3x – 2y = 8 ....................................... a 3. 4x – 3y = –13 ................................... a
3x + y = 5 ........................................ b x – 5y = 1 ........................................ b

Daripada / From b, y = 5 – 3x ....... c Daripada / From b, x = 1 + 5y ....... c
Gantikan c ke dalam a. Gantikan c ke dalam a.
Substitute c into a. Substitute c into a.
3x – 2(5 – 3x) = 8 4(1 + 5y) – 3y = –13
3x – 10 + 6x = 8 4 + 20y – 3y = –13
9x – 10 = 8 4 + 17y = –13
9x = 8 + 10 17y = –13 – 4
9x = 18 17y = –17
x = 2 y = –1

Gantikan x = 2 ke dalam c. Gantikan y = –1 ke dalam c.
Substitute x = 2 into c. Substitute y = –1 into c.
y = 5 – 3(2) x = 1 + 5(–1)
= 5 – 6 = 1 – 5
= –1 = – 4

Maka / Thus, x = 2 dan / and y = –1. Maka / Thus, x = – 4 dan / and y = –1.

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