CROSS MULTIPLICATION METHOD

Cross Multiplication Method :

This is one of the methods we use to solve system of linear equations.

Let us consider the following system of linear equations. 

a₁x + b₁y + c₁  =  0

a₂x + b₂y + c₂  =  0

We have to write the coefficients of the equations and do cross multiplication as shown below. 

We write the coefficient of y and constant term and two more columns by repeating the coefficients of x and y as follows. 

The result is given by

The solution is

Cross Multiplication Method - Examples

Example 1 :

Solve the following system of equations using cross multiplication method :

2x + 7y - 5  =  0

-3x + 8y  =  -11

Solution:

First we have to change the given linear equations in the form a₁x + b₁y + c₁  =  0, a₂x + b₂y + c₂  =  0.

2x + 7y - 5  =  0

-3x + 8y + 11  =  0

x/(77 + 40)  =  y/(15 - 22)  =  1/[16 + 21]

x/117  =  y/(-7)  =  1/37

Therefore the solution is (117/37, -7/37).

Example 2 :

Solve the following system of equations using cross multiplication method :

3x + 4y  =  24

20x - 11y  =  47

Solution:

First we have to make the given equations in the form of a₁x + b₁y + c₁  =  0, a₂x + b₂y + c₂  =  0.

3x + 4y - 24  =  0    ----- (1)

20x - 11y - 47  =  0 ----- (2)

x/(-188 - 264)  =  y/(-480 - (-141))  =  1/(-33 - 80)

x/(-452)  =  y/(-480+141))  =  1/(-33-80)

x/(-452)  =  y/(-339)  =  1/(-113)

Therefore solution is (4, 3).

After having gone through the stuff given above, we hope that the students would have understood how to solve system of equations using cross multiplication method.

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