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Question

Solve: $$2(ax - by)+ a + 4b = 0$$
           $$2(bx + ay) + b - 4a = 0$$


Solution

Given,  $$2(ax - by)+ a + 4b = 0$$ or, $$ax-by+\dfrac{a+4b}{2}=0$$......(1) and $$(bx + ay) +\dfrac{ b - 4a}{2} = 0$$.......(2).
Now (1)$$\times a+$$ (2)$$\times b$$ gives
$$(a^2+b^2)x+\dfrac{a^2+b^2}{2}=0$$
or, $$x=-\dfrac{1}{2}$$.
Now putting the value of $$x$$ in (1) we get, $$y=2$$.
So $$x=-\dfrac{1}{2}$$ and $$y=2$$.

Mathematics

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