Question

Solve for x and y:
`x + y = a + b, ax - by = a^2 - b^2`

Answer 1

The given equations are
x + y = a + b          ………(i)
`ax - by = a^2 - b^2`    ………(ii)
From (i)
y = a + b - x
Substituting y = a + b - x in (ii), we get
`ax – b(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 (i) to get
a + y = a + b
⇒y = b
Hence, x = a and y = b.