Point of Intersection Calculator
When two lines or more than two lines cross each other in a plane, this is called the intersection of lines, and the lines are called intersecting lines. They have a common point called the point of intersection.
What is the Point of Intersection Calculator?
'Point of Intersection Calculator' is an online tool that helps to calculate the value of intersection points for the given equations. Online Point of Intersection Calculator helps you to calculate the value of intersection points for the given equations in a few seconds.
Point of Intersection Calculator
How to Use Point of Intersection Calculator?
Please follow the steps below on how to use the calculator:
- Step 1: Enter the coefficients of equations in the given input box.
- Step 2: Click on the "Calculate" button to find the value of the intersection point.
- Step 3: Click on the "Reset" button to clear the fields and enter new values.
How to Find Point of Intersection?
When two lines share exactly one common point, they are called intersecting lines. The intersecting lines share a common point. And, this common point that exists on all intersecting lines is called the point of intersection.
An equation of the form Ax + By = C. Here, x and y are variables, and A, B, and C are constants.
To solve the point of intersection of the given equations, let's see an example to understand briefly
Solved Examples on Point of Intersection Calculator
Example 1:
Solve 2x + y = 7 and x + y = 5
Solution:
2x + y = 7 ------> (1)
x + y = 5 -------> (2)
From (2), x = 5 - y ------> (3)
Substitute (3) in (1),
2(5 - y) + y = 7
10 - 2y + y = 7
10 - y = 7
y = 3 ------> (4)
Substitute (4) in (2),
x + 3 = 5
x = 2
Therefore, point of intersection (x, y) = (2, 3)
Example 2:
Solve 3x - 2y = 4 and 4x - y = 7
Solution:
3x - 2y = 4 ------> (1)
4x - y = 7 -------> (2)
From (2), y = 4x - 7 ------> (3)
Substitute (3) in (1),
3x - 2(4x - 7) = 4
3x - 8x + 14 = 4
-5x = -10
x = 2 ------> (4)
Substitute (4) in (2),
4x - y = 7
4(2) - y = 7
8 - y = 7
y = 1
Therefore, x = 2, y = 1
Similarly, you can try the calculator to find the value of intersection point for the given equations:
- 7x + 8y = 17 and x - 16y = 4
- 11x - 17y = -18 and 12x - 15y = 8