Question

On comparing the ratios `bb(a_1/a_2, b_1/b_2)` and `bb(c_1/c_2)`, find out whether the following pair of linear equations are consistent, or inconsistent.

2x – 3y = 8 ; 4x – 6y = 9

Answer 1

2x - 3y = 8; 4x - 6y = 9

a₁ = 2, b₁ = -3, c₁ = 8

a₂ = 4, b₂ = -6, c₂ = 9

`a_1/a_2 = 2/4 = 1/2, b_1/b_2 = (-3)/(-6) = 1/2, c_1/c_2 = 8/9`

Here, `1/2 = 1/2 ≠ 8/9`

∴ `a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

Since `a_1/a_2 = b_1/b_2 ≠ c_1/c_2` these lines are parallel and hence the pair of linear equations are inconsistent.