Question

Solve the equation by substitution method :

(a+b)x + (a+b)y = 2a² -2b²

(a+b) (x + y) = 4ab

Answer 1

Dear student,
The equations you have given is wrong. If you expand the second equation you will get the same LHS as in the first eqn. So it turns out to be two equations have two different solutions. Kindly check the question properly, if the textbook has the same eqn, then ask help of your teacher. The possible eqn and the answer are given below.

take the second eqn
(a+b)(x+y)=4ab
=(a+b)x + (a+b)y = 4ab
=(a+b)x= 4ab - (a+b)y

Substituting in the first eqn.;
(a+b)x -(a+b)y = 2a² - 2b²

= 4ab - (a+b)y - (a+b)y = 2(a²-b²)

= 4ab -2(a+b)y = 2(a²-b²)
= 4ab-2(a²-b²) = 2(a+b)y
= 2ab-(a²-b²) = (a+b)y
= 2ab-a²+b² = (a+b)y

Adding and subtracting a² on LHS:

= 2ab-a²+b²+a²-a² = (a+b)y
= (a²+b²+2ab)- a²-a²= (a+b)y

= (a+b)² - 2a² = (a+b)y
= y = (a+b) - 2a²/(a+b)


Now substituting in first equation:
(a+b)x = 4ab- (a+b)y
=(a+b)x = 4ab - (a+b)[(a+b)-2a²/(a+b)]

= (a+b)x = 4ab - (a+b)² +2a²
Expanding rhs;
= (a+b)x = a²-b²+2ab
Adding and subtracting b² to rhs

= (a+b) x = (a²+b²+ 2ab)-b² -b²

= (a+b)x = (a+b)² -2b²

=x = (a+b) - 2b²/(a+b)