Expert: Josh - 11/24/2007

Question
sir please tell me that what will be the solution set of two parallel lines?
do they have 1) finite solution 2) infinite solution 3) no solution 4)one solution
set
please please reply me sooon thanks


Answer
Aliya,

According to the definition given in [1], a solution set is a set of possible values that a variable can take on in order to satisfy a given set of conditions.

When you say "the solution set of two parallel lines", I assume you mean the intersection between two parallel lines y=m*x+b and y=m*x+c. That is, we seek m*x+b = m*x+c.

Expressing this requirement in terms of a polynomial f(x)=0, where f(x)=b-c, first, we observe that this has no solution unless b=c. i.e., unless the two parallel lines are in fact one and the same. In this case, the variable x is not constrained and we have an infinite set of solutions since f(x)=b-c=0 is independent of x. In general, however, there is no solution to f(x)=b-c=0 when b is different from c. No x-value in R will satisfy this condition. This means two parallel lines do not intersect irrespective of the x value.

Reference:
[1] http://en.wikipedia.org/wiki/Solution_set