# FINDING THE POINT OF INTERSECTION OF TWO LINES EXAMPLES

Finding the Point of Intersection of Two Lines Examples :

If two straight lines are not parallel then they will meet at a point.This common point for both straight lines is called the point of intersection.

If the equations of two intersecting straight lines are given then their intersecting point is obtained by solving equations simultaneously.

## Finding the Point of Intersection of Two Lines Examples

Example 1 :

Find the intersection point of the straight lines

3 x + 5 y - 6  =  0  and 5x - y - 10  =  0

Solution :

3x + 5y - 6  =  0 ----- (1)

5x - y - 10  =  0   ------(2)

(2)  5  ==>   25 x - 5 y - 50 = 0

3x + 5y - 6  =  0

25x - 5y - 50  =  0

------------------

28 x - 56  =  0

28x  =  56

x  =  2

By applying x  =  2 in (1), we get

3x + 5y - 6  =  0

3(2) - 6 + 5 y  =  0

6 - 6 + 5 y  =  0

5y  =  0

y  =  0

So, the point of intersection of the straight lines is (2, 0).

Example 2 :

Find the intersection point of the straight lines

2x + 3y  =  5 and 3x + 4y  =  7

Solution :

2x + 3y = 5 ----- (1)

3x + 4y = 7  ------(2)

(1) ⋅ 4 =>  8x + 12y  =  20

(2) ⋅ 3 => 9x + 12y  =  21

8 x + 12 y = 20

9 x + 12 y = 21

(-)   (-)    (-)

--------------------

- 1 x   = - 1

x  =  1

By applying x  =  1 in (1), we get

8(1) + 12y  =  20

8 + 12 y  =  20

12 y  =  20 - 8

12 y  =  12

y  =  1

So the point of intersection of the straight lines is (1, 1).

Example 3 :

Find the intersection point of the straight lines

5x + 6y  =  25 and 3x - 4y  =  10

Solution :

5x + 6y  =  25 ----- (1)

3x - 4y  =  10  ------(2)

(1) ⋅ 2 =>  10 x + 12 y = 50

(2) ⋅ 3 =>  9 x - 12 y = 30

10x + 12y  =  50

9x - 12y  =  30

--------------------

19 x  =  80

x  =  80/19

By applying x = 80/19 in (1), we get

5 (80/19) + 6 y  =  25

400/19 + 6 y  =  25

(400 + 114y)/19  =  25

400 + 114 y  =  25  19

400 + 114 y  =  475

114 y  =  475 - 400

114 y  =  75

y  =  75/114

y  =  25/38

So, the point of intersection of the straight lines is

(80/19, 25/38).

After having gone through the stuff given above, we hope that the students would have understood how to find the point of intersection of two lines.

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