Introduction:

In geometry and algebra, the intersection of two lines refers to the point where two lines on a Cartesian coordinate system meet or cross each other. This concept is important in solving systems of linear equations.



Understanding Intersection of Two Lines:



When two lines intersect, they share a common point, which is the point of intersection.

In a coordinate system, this point is expressed as (x, y).

Finding the Intersection Point:



To find the intersection point, you need to solve a system of two linear equations representing the lines.

The solution to these equations gives the coordinates of the intersection point.

Example:



Consider two lines represented by the equations y = 2x + 3 and y = -x + 5.

To find the intersection point, set the equations equal to each other: 2x + 3 = -x + 5.

Solve for x: 3x = 2, x = 2/3.

Substitute x = 2/3 into one of the equations to find y: y = 2(2/3) + 3 = 10/3.

The intersection point is (2/3, 10/3).

Key Points to Remember:



The intersection point is where the two lines have the same x and y values.

If the lines are parallel, they do not intersect and have no common point.