Question

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

x + 3y = 11, 2(2x + 6y) = 22

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]

No.

The given pair of linear equations

x + 3y = 11 and 2x + 6y = 11

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

We get,

a₁ = 1, b₁ = 3, c₁ = 11

a₂ = 2, b₂ = 6, c₂ = 11

`a_1/a_2 = 1/2`

`b_1/b_2 = 1/2`

`c_1/c_2` = 1

Here, `a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

Hence, the given pair of linear equations has no solution.