solve simultaneous equation:ax+by=a+b;bx=ay+a+b where'a'and'b'are constant,where both are not zero

Question

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Answer 1

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)