Question

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

Answer 1

(i) x + y = 14 (1)

x − y = 4 (2)

From (1), we obtain

x = 14 − y (3)

Substituting this value in equation (2), we obtain

Substituting this in equation (3), we obtain

(ii)

From (1), we obtain

Substituting this value in equation (2), we obtain

Substituting in equation (3), we obtain

s = 9

s = 9, t = 6

(iii)3x − y = 3 (1)

9x − 3y = 9 (2)

From (1), we obtain

y = 3x − 3 (3)

Substituting this value in equation (2), we obtain

9 = 9

This is always true.

Hence, the given pair of equations has infinite possible solutions and the relation between these variables can be given by

y = 3x − 3

Therefore, one of its possible solutions is x = 1, y = 0.

(iv)

From equation (1), we obtain

Substituting this value in equation (2), we obtain

Substituting this value in equation (3), we obtain

(v)

From equation (1), we obtain

Substituting this value in equation (2), we obtain

Substituting this value in equation (3), we obtain

x = 0

x = 0, y = 0

(vi)

From equation (1), we obtain

Substituting this value in equation (2), we obtain

Substituting this value in equation (3), we obtain

Hence, x = 2, y = 3