Question

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

–3x – 4y = 12, 4y + 3x = 12

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

– 3x – 4y – 12 = 0 and 4y + 3x – 12 = 0

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

We get,

a₁ = – 3, b₁ = – 4, c₁ = – 12

a₂ = 3, b₂ = 4, c₂ = – 12

`a_1/a_2 = - 3/3` = – 1

`b_1/b_2 = - 4/4` = – 1

`c_1 /c_2 = (-12)/-12` = 1

Here, `a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

Hence, the pair of linear equations has no solution, i.e., inconsistent.