Question

On comparing the ratios `a_1/a_2,b_1/b_2` and `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 `a_1 x + b_1 y + c_1 = 0 and a_2 x + b_2 y + c_2 = 0`

 we have

`a1 = 9, b_1 = 3, c_1 = 12;`

`a_2 = 18, b_2 = 6, c_2 = 24`

`:.a_1/a_2=9/18=1/2,b_1/b_2=3/6=1/2`

`=>a_1/a_2=b_1/b_2=c_1/c_2`

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