If we have two lines in space then there can be three possibilities of solutions:
1: There can be only one intersection Point.
2: There can be infinite number of intersection points.
3: There can be no intersection point.
Let us see these three conditions:
1: Suppose we have two different line equations and these two lines are having same 'y' intercepts but slopes of these two lines are different then these two lines will have one intersection point. y- intercept is common in both of line equations so intersection point will be equals to y- intercept.
Let us take an example to understand this concept. Assume we have two equations of lines as y = -2x + 3 and y = ½ x + 3. Here in these two equations, slopes are different as -2 and ½ but y- intercept is 3 in both equation. So the intersection point will be equals to y- intercept 3.
2: If both line equations have same y- intercept points and same Slope then these two lines are same. They will overlap each other. So number of intersection points will be infinite. In this condition each point is the intersection point for lines.
3: If we have two line equations and Slope is same for both lines but y- intercept is different in both equations then in this situation these two lines are parallel to each other. These lines will never intersect each other and there will be no intersection point.