sir are the pair of linear eqations with intersecting lines only consistant

Yes, two linear equations have a common solution if the lines represnted by them are intersecting.

 

Note: A linear equation in x and y always represents a straight line.

Two straight lines are either parallel or intersecting.

Thus only intersecting lines have a common solution.

 

Now consider 3 linear equations in x and y.

We say they are consistent, if they have a common solution.

In geometry we say the lines are concurrent.