Question

solve for x and y: (a-b)x+(a+b)y=a^2-2ab-b^2 (a+b)(x+y)=a^2+b^2

Answer 1

ANSWER:

• Value of x is (a+b)
• Value of y is -2ab/(a+b)

GIVEN:

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

TO FIND:

• Value of x and y.

SOLUTION:

=> (a-b)x+(a+b)y = a²-2ab-b² .....(i)

=> (a+b)(x+y) = a²+b²

=> (a+b)x+(a+b)y = a²+b² .....(ii)

Subtracting eq (i) from (ii)

=> (a+b)x-(a-b)x = a²+b² -(a²-2ab-b²)

=> (a+b)x -(a-b)x = a²+b²-a²+2ab+b²

=> ax+bx-ax+bx = 2b²+2ab

=> 2bx = 2b(a+b)

=> x = (a+b)

Putting x = (a+b) in eq(i)

=> (a-b)(a+b)+(a+b)y = a²-2ab-b²

=> a²-b²+(a+b)y = a²-2ab-b²

=> (a+b)y = -2ab

=> y = -2ab/(a+b)

Value of x is (a+b)

Value of y is -2ab/(a+b)