Answer :

We have



and


Where x + 2y ≠ 0 and 3x - 2y ≠ 0


Lets simplify these equations. Assuming and



Multiply it with 6, we get


3p + 10q = -9 …(i)


Also,



Multiply it with 20, we get


25p – 12q = 61/3


75 – 36q = 61 …(ii)


To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.


Multiply equation (i) by 36 and equation (ii) by 10, so that the variables p and q in both the equations have same coefficients.


Recalling equations (i) and (ii),


3p + 10q = -9 [×36


75p – 36q = 61 [×10



858p = 286


p = 286/858 = 1/3


Substitute p = 1/3 in eq.(i)/eq.(ii), as per convenience of solving.


Thus, substituting in eq.(i), we get


3(1/3) + 10q = -9


1 + 10q = -9


10q = -9-1 = -10


q = -1


Thus, p=1/3 and q=-1


As p = 1/(x + 2y),



x + 2y = 3 …(iii)


And q = 1/(3x – 2y)



2y – 3x = 1 …(iv)


Subtracting equations (iii) and (iv) to obtain x and y,


(x + 2y) – (2y – 3x) = 3 – 1


x + 2y – 2y + 3x = 2


4x = 2


x = 1/2


Putting the value of x in equation (iv), we get


2y – 3(1/2) = 1


4y – 3 = 2


4y = 2 + 3 = 5


y = 5/4


Hence, we have x=1/2 and y=5/4


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