QUESTION: solve simultaneous equation:ax+by=a+b;bx=ay+a+b where'a'and'b'are constant,where both are not zero .
ax+by=a+b ------------------ (1)
bx=ay+a+b ------------------ (2)
(1)*b, (2)*a
ab.x = -b^2.y + ab + b^2 ------------- (3)
ab.x= a^2.y + a^2 + ab ------------- (4)
(4) - (3)
0 = (a^2 + b^2)y + a^2 - b^2
y = -(a^2 - b^2)/(a^2 + b^2)
Substitute for y = -(a^2 - b^2)/(a^2 + b^2) into (1),
ax - b(a^2 - b^2)/(a^2 + b^2) = a + b
ax(a^2 + b^2) - b(a^2 - b^2) = (a + b)(a^2 + b^2)
ax(a^2 + b^2) = (a)(a^2 + b^2) + (b)(a^2 + b^2) + b(a^2 - b^2) = (a)(a^2 + b^2) + (b)(2a^2)
x = 1 + 2ab/(a^2 + b^2)
x = (a + b)^2/(a^2 + b^2)
Answer: x = (a + b)^2/(a^2 + b^2), y = -(a^2 - b^2)/(a^2 + b^2)