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)

Multiplying (i) by b and adding it with (ii), we get

bx + ax = ab + b² + a² – b²

⇒ `x = (ab + a^2)/(a + b) = a`

Substituting x = a in (i), we have

a + y = a + b

⇒ y = b

Hence, x = a and y = b.