Answer
See the explanation
Work Step by Step
$\begin{cases}
ax+by=0\\
a^2x+b^2y=1, (a\ne0,b\ne0,a\ne b)
\end{cases}$
Multiplying first equation by $-a$ and adding it together.
$\begin{cases}
-a^2x-aby=0\\
a^2x+b^2y=1\\
-- -- -- -\\
(b^2-ab)y=1
\end{cases}$
Thus, $y=\frac{1}{b^2-ab}$.
Substituting back in, $ax+\frac{1}{b-a}=0,$
$ax=-\frac{1}{b-a},$ Dividing both sides by $-a$.
$x=-\frac{1}{ab-a^2},$
