Two lines are said to be intersecting lines if they have a common point. It is to be noted that if two straight lines intersect each other, they can intersect at exactly point and that point is said to be the intersecting point of those two lines.
Intersecting Lines
In the figure, there are two lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are two straight lines and P is a common point. Here, we say that the straight lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are intersecting at the point P and the point P is called the intersecting point of those two lines.

In a two dimensional plane, on the basis of this concept, any pair of straight lines can be categorized into the following cases:
1) Intersecting Lines
2) Non-intersecting Lines
3) Coincident Lines

It is to be noted that two or more lines can intersect at a single point. In such situations, we say that those lines are concurrent. It is to be noted that any pair of concurrent lines are intersecting lines, but pairs of intersecting lines may not concurrent. This fact is illustrated in the following diagram.
Intersecting Lines Definition

It is clear that the intersection of two straight lines is always a point and two lines can intersect at only one point, or they may coincident with each other.
The general equation of a straight line is of the form ax + by + c = 0,
where a, b, and c are real numbers. Now, consider two straight lines

a$_1$x + b$_1$y + c$_1$ = 0
a$_2$x + b$_2$y + c$_2$ = 0

Let P(x$_o$, y$_o$) be the intersecting point. Then, as the point is on both the lines, we have
a$_1$x$_o$ + b$_1$y$_o$ + c$_1$ = 0 (1)
a$_2$x$_o$ + b$_2$y$_o$ + c$_2$ = 0 (2)