Question

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

2x + 4y = 3, 12y + 6x = 6

Answer 1

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

Yes.

Given pair of equations are,

2x + 4y – 3 = 0 and 6x + 12y – 6 = 0

Comparing the equations with ax + by + c = 0

We get,

a₁ = 2, b₁ = 4, c₁ = – 3

a₂ = 6, b₂ = 12, c₂ = – 6

`a_1/a_2 = 2/6 = 1/3`

`b_1/b_2 = 4/12 = 1/3`

`c_1/c_2 = (-3)/-6 = 1/2`

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.