Solve the following system of equations :
(a + c) x - (a - c)y = 2ab;
(a + b) x - (a - b)y =2ab.

(a+c) x - (a-c)y = 2ab … (i)
(a+b) x - (a-b)y = 2ab … (ii)
Multiplying (ii) by (a+c) and (i) by (a+b), and subtracting,
(a+b)(a+c) x - (a+b)(a-c)y = 2ab(a+b) … (iii)
(a+b)(a+c) x - (a-b)(a+c)y = 2ab(a+c) … (iv)
Subtracting (iii) and (iv)
-(a+b)(a-c)y + (a-b)(a+c)y = 2ab(a + b) – 2ab(a + c)
(-a ² - ab+ ac+ bc+ a ² + ac – ab – bc )y = 2ab(a + b – a – c)
-2a(b - c)y = 2ab(b - c)
⇒ y = -b;
Substituting y = -b in (i),
(a + c)x – (a-c)(-b) = 2ab;
(a+ c)x = 2ab-ab+bc
= ab + bc
= b(a +c)
x = b
. ^. . The solution set is {b, -b}.