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 = a² + b²   ...(ii)

From (i),

`y = (bx)/a`

Substituting `y = (bx)/a` in (ii), we get

`ax + (b xx bx)/a = a^2 + b^2`

⇒ `x = ((a^2 + b^2) xx a)/(a^2 + b^2 ) = a`

Now, substitute x = a in (ii) to get

a² + by = a² + b²

⇒ by = b²

⇒ y = b

Hence, x = a and y = b.