Solving Simultaneous Equations by the Interchanged Coefficients Method :-


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Example No # 2

For example, suppose we have the following equations :
(11/4)x - (7/2)y = 36
-182x + 143y = 247

Here, we first simplify and re-arrange the above both equations as follows :
First equation :
(11/4)x - (7/2)y  = 36
(11/4)x - (14/4)y = 36
Therefore, 11x - 14y = 144

Second equation :
-182x + 143y = 247
Dividing by 13 throughout, we get
-14x + 11y = 19
Therefore, 14x - 11y = -19

Now, adding the above two simplified equations, we get :
25x - 25y = 125
→  x - y = 5
→  x = y + 5
And subtracting the two simplified equations, we get :
-3x - 3y = 163
→  3x + 3y = -163

Substituting the value of 'x' from above, we get :
Therefore, 3(y + 5) + 3y = -163
  6y + 15 = -163
   y = -(178/6) = -(89/3)

Therefore, x = y + 5 = -(89/3) + 5 =-(74/3)
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