Question

x+y=a+b
ax+by=a^2+b^2
find the values of a and b.

Answer 1

Here is the solution

(x+y) =(a+b) -------------(1)

ax-by =a2-b2 ----------------(2)

Multiplying eq (1) by b and adding (1)and (2)

(bx+by)+(ax-by) = (ab +b2)+(a2-b2)

x(a+b) = ab+a2

x(a+b)= a(a+b)

x=a

Putting this value in eq (1)

a+y=a+b

y=b

Hence x=a and y=b