Question

Do the following equations represent a pair of coincident lines? Justify your answer.

`3x + 1/7 y = 3, 7x + 3y = 7`

Answer 1

Condition for coincident lines,

`a_1/a_2 = b_1/b_2 = c_1/c_2`

No.

Given pair of linear equations are

`3x + 1/7y` = 3

7x + 3y = 7

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

Here, a₁ = 3, b₁ = `1/7`, c₁ = – 3

And a₂ = 7, b₂ = 3, c₂ = – 7

`a_1/a_2 = 3/7`

`b_1/b_2 = 1/21`

`c_1/c_2 = (-3)/(-7) = 3/7`

Here, `a_1/a_2 ≠ b_1/b_2`

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