Question

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

`3x + y - 3 = 0, 2x + 2/3y = 2`

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,

3x + y – 3 = 0

`2x + 2/3y` = 2

Comparing the equations with ax + by + c = 0

We get,

a₁ = 3, b₁ = 1, c₁ = – 3

a₂ = 2, b₂ = `2/3`, c₂ = – 2

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

`b_1/b_2 = 4/12 = 3/2`

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

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

i.e coincident lines