What is the Formula of Unique Solution?

Answer: The following set of equations has been provided: I 3x+5y=12… (ii) 5x+3y=4… (ii) We will use the method of elimination to solve the pair of equations that we have been given.

Therefore, by multiplying the first equation by three, we get the result 9x+15y=36. (iii)

Also, by multiplying equation (ii) by 5, we get

 25x+15y=20

 … (iv)

On subtracting (iii) from (iv), we get

  (25x+15y)−(9x+15y)=20−36

 ∴25x+15y−9x−15y=−16

 ∴16x=−16

 ∴x=−1

On substituting the value of x in equation (ii), we get

5(−1)+3y=4

 ∴−5+3y=4

 ∴3y=4+5

 ∴3y=9

 ∴y=3

Thus, we get x=−1

 and y=3

 , i.e. (x, y) =(−1,3)

 , which is a unique solution