The above mentioned Method is the Actual Way of Doing it . If You read it once Again You will Understand
Firstly we are arranging the equation to take common out of x and y part
and then to solve the equation we are multiplying by a+b to first equation and by a-b to second equation so as to solve the equation (to make common terms)
from that solved part we get the value of x
and when we put the value of x in either one of the equation . we get the value of y. There is nowhere to be confused
The above mentioned is the best possible solution
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