Question

Do the following pair of linear equations have no solution? Justify your answer.

x = 2y, y = 2x

Answer 1

The Condition for no solution = `a_1/a_2 = b_1/b_2 ≠ c_1/c_2`   .....(Parallel lines)

No.

Given pair of equations,

x = 2y or x – 2y = 0

y = 2x or 2x – y = 0

Comparing the equations with ax + by + c = 0

We get,

a₁ = 1, b₁ = – 2, c₁ = 0

a₂ = 2, b₂ = – 1, c₂ = 0

`a_1/a_2 = 1/2`

`b_1/b_2 = (-2)/-1` = 2

Here, `a_1/a_2 ≠ b_1/b_2`

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