Question

On comparing the ratios `bb(a_1/a_2,b_1/b_2)` and `bb(c_1/c_2)` without drawing them, find out whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincide.

6x – 3y + 10 = 0,

2x – y + 9 = 0

Answer 1

6x - 3y + 10 = 0    ...(i)

2x - y + 9 = 0       ...(ii)

a₁ = 6, b₁ = -3, c₁ = 10

a₂ = 2, b₂ = -1, c₂ = 9

`a_1/a_2 = 6/2 = 3/1, b_1/b_2 = (-3)/(-1) = 3/1, c_1/c_2 = 10/9`

Here, `3/1 = 3/1 ≠ 10/9`

∴ `a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

So when `a_1/a_2 = b_1/b_2 ≠ c_1/c_2` then the lines are parallel for the given pair of equations is. Hence, it is parallel.