6.4.4 Linear Equations, PT3 Focus Practice
Question 10:
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 11:
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 12:
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 13:
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