CROSS MULTIPLICATION METHOD

About "Cross Multiplication Method"

Cross Multiplication Method :

This is the method which can be used to solve 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.

That is we have to bring the constants with x, y terms.

2 x + 7 y - 5 = 0

-3 x + 8 y + 11 = 0

x/[(7(11) - (8) (-5)] = y/[(-5(-3) - (2) (11)] = 1/[(2(8) - (-3) (7)]

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 a₁ x + b₁ y + c₁ = 0,a₂ x + b₂ y + c₂ = 0.

3 x + 4 y - 24 = 0    ----- (1)

20 x - 11 y - 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).

Verification:

Now let us apply the answer that we got in the first or second equation to check whether we got correct answer or not.

3 x + 4 y = 24

3(4) + 4(3) = 24

12 + 12 = 24

 24 = 24

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