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.

5x – 4y + 8 = 0,

7x + 6y – 9 = 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 = 5, b₁ = – 4, c₁ = 8;

a₂ = 7, b₂ = 6, c₂ = – 9

`:.a_1/a_2=5/7,b_1/b_2=(-4)/6,c_1/c_2 = 8/(-9)`

`=>a_1/a_2!=b_1/b_2`

Thus, the lines representing the pair of linear equations are intersecting.