Question

Solve the following pair of linear equations by the substitution method.

(i) x + y = 14
x – y = 4

(ii) 3x – y = 3
9x – 3y = 9​

Answer 1

(i) Given,

x + y = 14 and x – y = 4 are the two equations.

From 1st equation, we get,

x = 14 – y

Now, put the value of x in second equation to get,

(14 – y) – y = 4

14 – 2y = 4

2y = 10

Or y = 5

By the value of y, we can now find the value of x;

∵ x = 14 – y

∴ x = 14 – 5

Or x = 9

Hence, x = 9 and y = 5.

(ii) Given,

3x – y = 3 and 9x – 3y = 9 are the two equations.

From 1st equation, we get,

x = (3 + y)/3

Now, substitute the value of x in the given second equation to get,

9[(3 + y)/3] – 3y = 9

⇒ 3(3+y) – 3y = 9

⇒ 9 + 3y – 3y = 9

⇒ 9 = 9

Therefore, y has infinite values and since, x = (3 + y)/3, so x also has infinite values.