In this page we are going to see how to find the 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.

Example 1

Find the intersection point of the straight lines 2x - 3y = 6 and

x + y = 3

Solution:

2x - 3y = 6 -----(1)

To make the coefficient of y of the second equation as 3 we need to multiply the the whole equation by 3.Then we are going to add the first equation with second equation.

(2) x 3 3x + 3y = 9

2x - 3y = 6

3x + 3y = 9

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

5x = 15

x = 15/5

x = 3

Substituting x = 3 in the first equation

2(3) - 3y = 6

6 -3y = 6

-3y = 6-6

-3y = 0

y = 0/3

y = 0

So the intersection point of the straight lines is (3,0).

Example 2

Find the intersection point of the straight lines 3x + 5y = 6 and

5x - y = 10

Solution:

Now we need to solve both the equation.

3x + 5y = 6 -----(1)

5x - y = 10 -----(2)

To
make the coefficient of y of the second equation as 5 we need to
multiply the the whole equation by 5.Then we are going to add the first
equation with second equation.

(2) x 5 25x - 5y = 50

3x + 5y = 6 -----(1)

25x - 5y = 50 -----(2)

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

28x = 56

x = 56/28

x = 2

Substituting x = 2 in the first equation

3(2) + 5y = 6

6 +5y = 6

5y = 6-6

5y = 0

y = 0/5

y = 0

So the answer is (2,0).

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