Question

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

Answer 1

Given, $2(ax-by)+a+4b=0$ or, $ax-by+\frac{a+4b}{2}=0$......(1) and $(bx+ay)+\frac{b-4a}{2}=0$.......(2).

Now (1)$\times a+$ (2)$\times b$ gives

$(a^2+b^2)x+\frac{a^2+b^2}{2}=0$

or, $x=-\frac{1}{2}$.

Now putting the value of $x$ in (1) we get, $y=2$.

So $x=-\frac{1}{2}$ and $y=2$.