- Two non-parallel lines in the same plane have one point of intersection.
- Two parallel lines in the same plane have no point of intersection.
- Two circles in the same plane can have zero, one or two points of intersection.
In a Cartesian plane, the coordinates of the point of intersection of two curves (such as two lines) may be found by solving the system of equations.
Consider the lines whose equations are y = x – 4 et y = –2x + 5; then, x – 4 = –2x + 5. These lines are represented in a Cartesian plane.
Therefore: 3x = 9 and x = 3
And: y = –1
The coordinates of the point of intersection of these lines are (3, –1).