HOW TO FIND POINT OF INTERSECTION OF TWO LINES

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 Point of Intersection of Two Lines - Examples

Example 1 :

Find the intersection point of the straight lines 

x - 5y + 17  =  0  and 2x + y + 1 = 0

Solution :

x - 5y + 17  =  0 ----- (1)

2x + y + 1  =  0  ------(2) 

(2)  5 ==> 10x + 5y + 5 = 0  ----(3)

                          x - 5 y + 17  =  0  

                       10 x + 5 y + 5  =  0

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

                        11 x  + 22  =  0

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

                        11 x   =  - 22

                          x  =  -2

By substituting x = -2 in (1), we get

 -2 - 5y + 17  =  0

15 - 5 y  =  0  

- 5y  =  - 15

-5y  =  - 15

y  =  3

So the intersection point of the straight lines is (-2, 3).

Example 2 :

Find the intersection point of the straight lines 

5x - 3y - 8  =  0  and  2x - 3y - 5  =  0

Solution :

5x - 3y - 8  =  0 ----- (1)

2x - 3y - 5  =  0 ------(2) 

5 x - 3 y - 8  =  0  

2 x - 3 y - 5  =  0

(-)  (+)  (+) 

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

3 x - 3  =  0

                          x  =  1

By applying x  =  1 in the first equation

5(1) - 3y - 8  =  0

5 - 8 - 3y  =  0 

-3 - 3y  =  0  

-3y  =  3

y  =  -1

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

Example 3 :

Find the intersection point of the straight lines

4x - 7y  =  0  and 8x - y - 26  =  0

Solution :

4x - 7y  =  0 ----- (1)

8x - y - 26  =  0  ------(2) 

(2)  7 =>   56 x - 7 y - 182 = 0

4x - 7y + 0  =  0  

56 x - 7y - 182  =  0

                               (-)     (+)    (+)

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

-52 x  + 182  =  0

x  =  -182/(-52)

x  =  7/2

By applying x  =  7/2 in (1), we get

-4(7/2) - 7 y  =  0

-14 - 7y  =  0

-7y  =  14

y  =  -2

So the point of intersection of the given lines is (7/2, -2).

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Operations with Negative Numbers Worksheet

    Jan 16, 22 11:40 PM

    Operations with Negative Numbers Worksheet

    Read More

  2. Operations with Negative Numbers

    Jan 16, 22 11:23 PM

    Operations with Negative Numbers

    Read More

  3. Playing with Numbers

    Jan 16, 22 08:14 PM

    Playing with Numbers

    Read More