1. Possible Intersection of Straight Lines

2. Then, how can I find the coordinates of their intersection?
Given two non-parallel lines L1 and L2, they must intersect.
Then, how can I find the coordinates of their intersection?

3. Consider the following two straight lines.
L1: x + y - 4 = 0 ……(1)
L2: x - y - 2 = 0 ……(2)
If (x0, y0) is the intersection of L1 and L2, then L1 L2 O y x
(x0, y0) satisfies both equations of L1 and L2.
(x0, y0) lies on  both L1 and L2.
(x0, y0)

4. Consider the following two straight lines.
L1: x + y - 4 = 0 ……(1)
L2: x - y - 2 = 0 ……(2)
Since the coordinates of the intersection satisfies both equations of L1 and L2,
we can solve to find the
coordinates of the intersection.

5. Consider the following two straight lines.
L1: x + y - 4 = 0 ……(1)
L2: x - y - 2 = 0 ……(2)
(1) + (2): 2x - 6 = 0
x = 3
By substituting x = 3 into (1), we have
3 + y - 4 = 0
y = 1
∴ L1 and L2 intersect at (3, 1).

6. Number of intersections of two straight lines
Case 1
Case 2
Case 3
Condition
unequal slopes
equal slope and
unequal y-intercepts
equal slope and equal y-intercept
No. of intersections
one intersection
no intersections
an infinite no. of intersections

7. Follow-up question
Determine the number of intersections between the two straight lines L1 : 3x + 2y - 5 = 0 and L2 : 6x + 2y - 3 = 0.
Slope of L1 = - 2 3
 For a straight line Ax + By + C = 0,
Slope of L2 = = - 2 6 ∵
Slope of L1  slope of L2
∴ L1 and L2 have one intersection.