Question

If in two linear equations ax + by = c and dx + ey = f and a/d = b/e = c/f then, which of the following is true about the two equations?
(a) They represents intersecting lines
(b) They represent coincident lines
(c) Have a unique solution
(d) None of these

Answer 1

They will represent A set of Parallel rays.

And In special condition they will coincident line. if ration will be =1.

Answer 2

Solution:

Consider two equations of line ,

1. 2 x +3 y=6

2. 4 x + 6 y =12

As, you can see that, $\frac{2}{4}=\frac{3}{6}=\frac{6}{12}$

2 ×Line 1=Line 2

both are same lines,means coincident.

a x + b y=c

d x + e y =f

$\frac{a}{d}=\frac{b}{e}=\frac{c}{f}$

It represent coincident lines →→Option B