This question is taken from linear equations in two variables and it was already asked in previous papers in which we have given two equations x/a+y/b=2, ax-by=a²-b² and we have to find the value of variables x and y

Kindly solve the above equations

RS Aggarwal, Class 10, chapter 3B, question no 41

Given equations are

x/a+y/b=2;ax−by=a²−b²

x/a+y/b=2

⇒ay+bx=2ab _________ (1)

ax−by=a²−b² _______ (2)

From (1) & (2)

Multiply (1) by ‘a’ (2) by ‘b’

abx+a²y=2a²b

abx−b²y=ba²−b³

– + –

________________________________

y(a²+b²)=2a²−ba²+b³

⇒y(a²+b²)=a²b+b³

⇒y=b [put in equation – 1]

We get

ay+bx=2ab

⇒a(b)+bx=2ab

⇒bx=2ab−ab

⇒bx=ab

⇒x=ab/b

⇒x=a