Answer :

We have,

6(ax + by) = 3a + 2b


6ax + 6by = 3a + 2b …(i)


6(bx – ay) = 3b – 2a


6bx – 6ay = 3b – 2a …(ii)


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


Lets multiply equation (i) by a and (ii) by b, so that variable y in both the equations have same coefficient.


Recalling equations 1 & 2,


6ax + 6by = 3a + 2b [×a]


6bx – 6ay = 3b – 2a [×b]



6a2x + 6b2x + 0 = 3a2 + 3b2


6(a2 + b2)x = 3(a2 + b2)


2x = 1


x = 1/2


Substitute x = 1/2 in equations (i)/(ii), as per convenience of solving.


Thus, substituting in equation (i), we get


6a(1/2) + 6by = 3a + 2b


3a + 6by = 3a + 2b


6by = 2b


y = 1/3


Hence, we have x = 1/2 and y = 1/3.


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