On comparing the ratios , and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide:
(i)
(ii)
(iii)
Two lines, a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
If , then the lines coincide
If , then the lines are parallel
If , then the lines intersect
(i)
Thus, .
The lines intersect.
(ii)
Thus,
The lines are coincident.
(iii)
Thus,
The lines are parallel.