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.

9x + 3y + 12 = 0

18x + 6y + 24 = 0

Answer 1

Comparing the given equations with standard forms of equations a₁ x + b₁ y + c₁ = 0 and a₂ x + b₂ y + c₂ = 0

We have

a₁ = 9, b₁ = 3, c₁ = 12;

a₂ = 18, b₂ = 6, c₂ = 24

`a_1/a_2 = 9/18, b_1/b_2 = 3/6, c_1/c_2 = 12/24`

`9/18 = 3/6 = 12/24 = 1/2`

∴ `a_1/a_2 = b_1/b_2 = c_1/c_2`

Thus, the lines representing the pair of linear equation coincide.