Question

Solve for x and y:

ax – by = a² + b², x + y = 2a

Answer 1

The given equations are

ax – by = a² + b²   ...(i)

x + y = 2a   ...(ii)

From (ii)

y = 2a – x

Substituting y = 2a – x in (i), we get

ax – b(2a – x) = a² + b²

⇒ ax – 2ab + bx = a² + b²

⇒ `x = (a^2 + b^2 + 2ab)/(a + b)`

= `((a + b)^2)/(a + b)`

= a + b

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

a + b + y = 2a

⇒ y = a – b

Hence, x = a + b and y = a – b.