11.2.1 Linear Equations II, PT3 Focus Practice
Question 1:
It is given that 2x = 6 and 3x + y = 10.
Calculate the value of y.
Solution:
2x = 6
x = 3
Substitute x = 3 into 3x + y = 10
3 (3) + y = 10
y = 10 – 9
y = 1
Question 2:
It is given that y = –1 and x – 3y = –10.
Calculate the value of x.
Solution:
Substitute y = –1 into x – 3y = –10
x – 3 (–1) = –10
x + 3 = –10
x = –10 – 3
x = –13
Question 3:
It is given that 7x – 2y = 19 and x + y = 13.
Calculate the value of y.
Solution:
Using Substitution method
7x – 2y = 19 -------- (1)
x + y = 13 ------- (2)
From equation (2),
x = 13 – y ------- (3)
Substitute equation (3) into equation (1),
7x – 2y = 19
7 (13 – y) – 2y = 19
91 – 7y – 2y = 19
– 9y = 19 – 91
– 9y = –72
y = 8
Question 4:
It is given that 2x – y = 5 and 3x – 2y = 8.
Calculate the value of x.
Solution:
Using Elimination method
2x – y = 5 -------- (1)
3x – 2y = 8 ------- (2)
(1) × 2: 4x – 2y = 10 -------- (3)
3x – 2y = 8 ------- (2)
(3) – (2): x – 0 = 2
x = 2
Question 5:
It is given that x + 2y = 4 and x + 6y = –4.
Calculate the value of x.
Solution:
Using Elimination method
x + 2y = 4 -------- (1)
x + 6y = –4 ------- (2)
(1) × 3: 3x + 6y = 12 -------- (3)
x + 6y = –4 ------- (2)
(3) – (2): 2x = 12 – (–4)
2x = 16
x = 8