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