Intersection of lines. Suppose that lines and in the plane are given by their equations. How can we find the coordinates of their intersection point?

Since the intersection point М belongs to the first line, if follows that its coordinates y

 

 

 

М

0 x

 

satisfy the equation of this line. On the other hand, the point М belongs to the second line, and its coordinates satisfy the second equation .

Thus, the coordinates of the intersection point satisfy both equations simultaneously:

To find the coordinates of the intersectionpoint of two lines, we must solve the system of equations.

Example. Find the intersection points of the line with the coordinates axes:

у

 

 

 

0 х

 

To find the intersection point of the line with the x–axis, we solve the system of equations

which implies F₁(x)=0.

Similarly the intersection points of the line and the y–axis are found from

i.e., F₁(y)=0.