Question

Solve for x and y:
`x/a - y/b = 0, ax + by = a^2 + b^2`

Answer 1

The given equations can be written as
`x/a - y/b = 0`                                        …….(i)
`ax + by = a^2 + b^2`                           ……(ii)
From (i),
`y = (bx)/a`
Substituting y = `(bx)/a` in (ii), we get
`ax + (b×bx)/a = a^2 + b^2`
`⇒ x = ((a^2+ b^2) ×a)/(a^2+ b^2 )= a`
Now, substitute x = a in (ii) to get
`a^2 + by = a^2 + b^2`
`⇒by = b^2`
⇒y = b
Hence, x = a and y = b.