and
coincidence lines if
But in parallel lines, the condition satisfy
Point of Intersection:
If two disticnt lines and
, represented by the equations
intersect at
then
Note:
then
(i) if then
and
intersect at one point and it have unique solution.
(ii) If , then
and
never intesect, where
and
are parallel lines and having no solution.
(iii) If , then
and
are coincidenc linea and having infinitel many solutions.
Examples for Corresponding Conditions:
(i)
(ii)
(iii)
Family of lines through the point of intersection of two lines:
Let -(i)
-(ii)
Now consider the equation -(iii), represents family or system of lines where
.
Conditions:
, represents family of lines.
(i) through the point of intersections and
, if they intersect.
(ii) parallel to and
, if they are parallel.
Examples for Corresponding Conditions: