Question

on comparing the ratio a¹/ a² b¹/b² and c¹/c² find out weather the pair of linear equation intersect at a point or parallel or coincident ​

Answer 1

Answer:

Let, the equations be a1x+b1y+c1=0 and a2x+b2y+c2=0

If a1/a2 is not equal to b1/b2 then the lines intersect at a point

If a1/a2 is equal to b1/b2 equal to c1/c2 then the lines are coincident

If a1/a2 is equal to b1/b2 and not equal to c1/c2 then the lines are parallel

Extra Information

If the lines intersect at a point then they are said to be consistent and have only one solution.

If lines are coincident then they are also said to be consistent and have infinitely many solutions.

If lines are parallel then they are said to be inconsistent and have no solution.