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Elimination Method

Elimination by Equating the Coefficients
In this method, we multiply both the equations by suitable non-zero constants so that the coefficients of the variable to be eliminated becomes equal. We now add or subtract the equations so that the variable with equal coefficients gets eliminated.  

Example

Solve     
1. 2x + 3y = 13                      2. 3x + 2y = 7
    5x + 2y = 16                          4x - 3y = -2

Solution

1. 2x + 3y = 13   .....(i)
    5x + 2y = 16  .....(ii)
Multiplying (i) by 5 and (ii) by 2, and we subtract (ii) from (i).
    10x + 15y  = 65
   -10x -  4y   = -32
            11y    = 33
                y = 3
Substituting value of y in (i)
We get 2x + 3(3) = 13
  2x = 4
    x = 2
Therefore, the solution is
x = 2, y = 3

2.  3x + 2y = 7  .....(i)
     4x - 3y = -2  .....(ii)
Multiplying (i) by 4 and (ii) by 3, we subtract (ii) from (i)
  12x + 8y = 28
 -12x + 9y = 6
         17y = 34
             y = 2
Putting this value of y in (i),
We get 3x + 2(2) = 7
                  3x = 3  
                 x = 1
Therefore, the solution is x = 1, y = 2   


 

Example

   

Solution

Let us assume    and    ...........(A)
The equations now become
2u + v = 2       ---------- (i)
  u - v = 4         ---------- (ii)
Adding (i) and (ii), we get
  3u = 6      
 u = 2
From(1)       2(2) + v = 2
          v = -2   
Now x = ua.....from (A)

Hence x = 2a,     

Now y = v .....from (A). 

Hence y = -2b
Therefore, the solution is x = 2a, y = -2b





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