290. Excluding the unknown $y$ from the system of equations

$$
\begin{aligned}
& a_{1} x+b_{1} y=c_{1} \\
& a_{2} x+b_{2} y=c_{2}
\end{aligned}
$$

we obtain

$$
x=\frac{c_{1} b_{2}-c_{2} b_{1}}{a_{1} b_{2}-a_{2} b_{1}}
$$

Write, without new calculations, the formula for $y$.
290. Our equations will not change if we replace $x$ with $y$ and $y$ with $x$ and simultaneously replace the coefficients $a$ and $b$ with the coefficients $b$ and $a$ with the corresponding indices; if the same is done with the formula for $x$, we get

$$
y=\frac{c_{1} a_{2}-c_{2} a_{1}}{b_{1} a_{2}-b_{2} a_{1}}
$$

Alternatively: both unknowns play the same role in our equations; the formula for $x$ can be read as follows: the value of the unknown is equal to a fraction, the numerator of which is the difference between the product of the known term of the first equation and the coefficient of the other unknown in the second equation and the product of the known term of the second equation and the coefficient of the other unknown in the first equation, and the denominator is the same difference, but with the known terms replaced by the corresponding coefficients of the determined unknown. In this form, the rule directly gives the formula for $y$.