Question

Show that the system 2x + 3y – 1= 0 and 4x + 6y – 4 = 0 has no solution.

Answer 1

The given system is

2x + 3y – 1 = 0   ...(i)

4x + 6y – 4 = 0   ...(ii)

Here, a₁ = 2, b₁ = 3, c₁ = –1, a₂ = 4, b₂ = 6 and c₂ = –4

Now,

`(a_1)/(a_2) = 2/4 = 1/2`

`(b_1)/(b_2) = 3/6 = 1/2`

`(c_1)/(c_2) = (-1)/(-4) = 1/4`

Thus, `(a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2 )` and therefore the given system has no solution.