Question

Solve x and y.
x+y=a+b
ax-by=a^2-b^2.

Answer 1

Answer:

Given,

x+y =a+b. ...... (1)

ax-by =a^2 -b^2 ...(2)

From eq.(1)

y=a+b-x.

Subtracting y=a+b-x in eq.( 2),we get,

ax-by(a+b-x)=a^2-b^2.

ax-ab-b^2+bx=a^2-b^2.

x=a^2+ab/a+b=a

Now substitute x=a in eq.2 to get a+y=a+b

Or y=b

Hence x=a and y=b.

Answer 2

x+y=a+b. (I)×b

ax-by=a^2-b^2. (ii)×1

bx+by=ab+b^2. (iii)

on adding ii&iii

x(a+b)=a^2+ab

x=a^2+ab/(a+b)

again (I)×a -(ii)

y(a+b)=ab+b^2

y=ab+b^2/(a+b)

hope it will help you