Question

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

`x/2 + y + 2/5` = 0, `4x + 8y + 5/16` = 0

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

`x/2 + y + 2/5` = 0

`4x + 8y + 5/16` = 0

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

Here, `a_1 =1/2, b_1 = 1, c_1 = 2/5`

And `a_2 = 4, b_2 = 8, c_2 = 5/16`

`a_1/a_2 = 1/8`

`b_1/b_2 = 1/8`

`c_1/c_2 = 32/25`

Here, `a_1/a_2 = b_1/b_2 ≠ c_1/c_2`,

i.e. parallel lines

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