Question

Solve the following pairs of equations by reducing them to a pair of linear equations:

Answer 1

Let and, then the equations change as follows.

Using cross-multiplication method, we obtain

Putting and in the given equations, we obtain

Multiplying equation (1) by 3, we obtain

6p + 9q = 6 (3)

Adding equation (2) and (3), we obtain

Putting in equation (1), we obtain

Hence,

Substituting in the given equations, we obtain

By cross-multiplication, we obtain

Putting and in the given equation, we obtain

Multiplying equation (1) by 3, we obtain

Adding (2) an (3), we obtain

Putting this value in equation (1), we obtain

Putting and in the given equation, we obtain

By cross-multiplication method, we obtain

Putting and in these equations, we obtain

By cross-multiplication method, we obtain

Hence, x = 1, y = 2

Putting and in the given equations, we obtain

Using cross-multiplication method, we obtain

Adding equation (3) and (4), we obtain

Substituting in equation (3), we obtain

y = 2

Hence, x = 3, y = 2

Putting in these equations, we obtain

Adding (1) and (2), we obtain

Substituting in (2), we obtain

Adding equations (3) and (4), we obtain

Substituting in (3), we obtain

Hence, x = 1, y = 1