Question

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

–2x – 3y = 1, 6y + 4x = – 2

Answer 1

Condition for coincident lines,

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

Yes,

Given pair of linear equations.

– 2x – 3y – 1 = 0 and 4x + 6y + 2 = 0

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

Here, a₁ = – 2, b₁ = – 3, c₁ = – 1

And a₂ = 4, b₂ = 6, c₂ = 2

`a_1/a_2 = -2/4 = -1/2`

`b_1/b_2 = - 3/6 = -1/2`

`c_1/c_2 = -1/2`

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

i.e. coincident lines

Hence, the given pair of linear equations is coincident.