**How to Find Point of Intersection of Two Lines without Graphing ?**

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)

(2) ⋅ 3 ==>3x + 3y = 9

2x - 3y = 6

3x + 3y = 9

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

5x = 15

x = 15/5

x = 3

By applying x = 3 in (1), we get

2(3) - 3y = 6

6 - 3y = 6

-3y = 0

y = 0

So the point of intersection of the given 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)

(2) ⋅ 5 ==> 25x - 5y = 50

3x + 5y = 6

25x - 5y = 50

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

28x = 56

x = 2

by applying x = 2 in (1), we get

3(2) + 5y = 6

6 + 5y = 6

5y = 6 - 6

5y = 0

y = 0

So the answer is (2, 0).

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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