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Substitution Method

Elimination by Substitution
In this method we first find the value of one variable (y), say in terms of x from the first equation and put this value of y in the second equation. Thus we get an equation in terms of x, which can easily be solved. The value of x is then put in the expression for y.     

 

Example

Solve
   (i) 2x - 3y = 5              (ii) x + 2y = 5
       3x + 2y = 1                  2x - y  = 5

Solution

(i) 2x - 3y = 5
      ⇒   y =
We substitute the value of y in
 3x + 2y = 1
⇒   3x + 2() = 1
⇒   9x + 2(2x-5) = 3
                  ⇒   13x = 13 
                    ⇒     x = 1
Putting this value of x in (ii) we get,
  ⇒  y =
Therefore, the solution is x = 1,y = -1
(ii)   x + 2y = 5
               x = 5 - 2y
We put this value of x in
            2x - y = 5
  ⇒ 2(5-2y) - y = 5
   ⇒ 10 - 4y - y = 5
    ⇒ 10 - 5y = 5   

                y = 1
Putting this value of y in (ii), we get
 x = 5 - 2(1) = 3
Therefore, the solution is          
x = 3, y = 1.





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