Question

Are the following pair of linear equations consistent? Justify your answer.

`3/5x - y = 1/2, 1/5x - 3y = 1/6`

Answer 1

Conditions for pair of linear equations to be consistent are:

`a_1/a_2 ≠ b_1/b_2` ......[Unique solution]

`a_1/a_2 = b_1/b_2 = c_1/c_2`......[Coincident or infinitely many solutions]

Yes.

The given pair of linear equations

`(3/5)x - y = 1/2`

`(1/5)x - 3y = 1/6`

Comparing the above equations with ax + by + c = 0

We get,

`a_1 = 3/5, b_1 = -1, c_1 = -1/2`

`a_2 = 1/5, b_2 = 3, c_2 = -1/6`

`a_1/a_2` = 3

`b_1/b_2 = (-1)/-3 = 1/3`

`c_1/c_2` = 3

Here, `a_1/a_2 ≠ b_1/b_2`

Hence, the given pair of linear equations has unique solution, i.e., consistent.