On comparing the ratios a1/a2,b1/b2 and c1/c2 , find out whether the lines representing the following pairs of linear equations intersect at a point,

(i) 5x − 4y + 8 = 0, 7x + 6y – 9 = 0

Comparing equation 5x − 4y + 8 = 0 with a₁x + b₁y + c₁ = 0and 7x + 6y – 9 = 0 with a₂x + b₂y + c₂ = 0,

(ii) 9x + 3y + 12 = 0, 18x + 6y + 24 = 0

Comparing equation 9x + 3y + 12 = 0 with a₁x + b₁y + c₁ = 0and 7x + 6y – 9 = 0 with a₂x + b₂y + c₂ = 0,

We get,

Hence, lines are coincident.

(iii) 6x − 3y + 10 = 0, 2x – y + 9 = 0

Comparing equation 6x − 3y + 10 = 0 with a₁x + b₁y + c₁ = 0and 7x + 6y – 9 = 0 with a₂x + b₂y + c₂ = 0,

Hence,
lines are parallel to each other.