Question

(3) Solve the following equations:
(a + c)x – (a – c)y= 2ab; (a + b)x – (a - b)y = 2ab​

Answer 1

Step-by-step explanation:

(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}.