Question

Solve for x and y:

x + y = a + b, ax – by = a² – b²

Answer 1

The given equations are

x + y = a + b   ...(i)

ax – by = a² – b²    ...(ii)

From (i)

y = a + b – x

Substituting y = a + b – x in (ii), we get

ax – b(a + b – x) = a² – b²

⇒ ax – ab – b² + bx = a² – b²

⇒ `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.