Question

Solve for x and y:
`x/a + y/b = a + b, x/(a^2)+ y/(b^2) = 2`

Answer 1

The given equations are
`x/a + y/b = a + b`               …….(i)
`x/(a^2)+ y/(b^2) = 2`                    ……(ii)

Multiplying (i) by b and (ii) by  `b^2` and subtracting, we get
`(bx)/a - (b^2x)/(a^2)= ab + b^2 - 2b^2`
`⇒(ab− b^2)/(a^2) x = ab - b^2`
`⇒x = ((ab− b^2)a^2)/(ab −b^2) = a^2`
Now, substituting x = `a^2` in (i) we get
`(a^2)/a + y/b = a + b`
`⇒y/b = a + b – a = b`
⇒y = `b^2`
Hence, x = `a^2 and y = b^2`.