Question

Solve the following pair of linear equations by the elimination method and the substitution method:

Answer 1

(i) By elimination method

Multiplying equation (1) by 2, we obtain

Subtracting equation (2) from equation (3), we obtain

Substituting the value in equation (1), we obtain

By substitution method

From equation (1), we obtain

(5)

Putting this value in equation (2), we obtain

−5y = −6

Substituting the value in equation (5), we obtain

(ii) By elimination method

Multiplying equation (2) by 2, we obtain

Adding equation (1) and (3), we obtain

Substituting in equation (1), we obtain

Hence, x = 2, y = 1

By substitution method

From equation (2), we obtain

(5)

Putting this value in equation (1), we obtain

7y = 7

Substituting the value in equation (5), we obtain

(iii) By elimination method

Multiplying equation (1) by 3, we obtain

Subtracting equation (3) from equation (2), we obtain

Substituting in equation (1), we obtain

∴

By substitution method

From equation (1), we obtain

(5)

Putting this value in equation (2), we obtain

Substituting the value in equation (5), we obtain

∴

(iv)By elimination method

Subtracting equation (2) from equation (1), we obtain

Substituting this value in equation (1), we obtain

Hence, x = 2, y = −3

By substitution method

From equation (2), we obtain

(5)

Putting this value in equation (1), we obtain

5y = −15

Substituting the value in equation (5), we obtain

∴ x = 2, y = −3