Question

Find whether the following pair of linear equations is consistent or inconsistent:

3x + 2y = 8

6x – 4y = 9

Answer 1

3x + 2y = 8

6x – 4y = 9

a₁ = 3, b₁ = 2, c₁ = 8

a₂ = 6, b₂ = –4, c₂ = 9

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

`b_1/b_2 = 2/-4 = (-1)/2`

`c_1/c_2 = 8/9`

`a_1/a_2 ≠ b_1/b_2`

The given pair of linear equations has unique solution.

So, the given pair of lines is consistent.