203. Find the condition for the compatibility of the equations:

$$
a_{1} x+b_{1} y=c_{1}, \quad a_{2} x+b_{2} y=c_{2}, \quad a_{3} x+b_{3} y=c_{3}
$$
Instruction. Assuming that the equations are consistent, transform the first two into the form:

$$
\left(a_{1} b_{2}-a_{2} b_{1}\right) x=c_{1} b_{2}-c_{2} b_{1}, \quad\left(a_{1} b_{2}-a_{2} b_{1}\right) y=a_{1} c_{2}-a_{2} c_{1}
$$

Determine the form of the values for $x$ and $y$ under the assumption that $a_{1} b_{2}-a_{2} b_{1} \neq 0$, and substitute the obtained expressions for $x$ and $y$ into the third equation. The desired condition will be:

$$
a_{1}\left(b_{2} c_{3}-b_{3} c_{2}\right)+a_{2}\left(b_{3} c_{1}-c_{3} b_{1}\right)+a_{3}\left(b_{1} c_{2}-b_{2} c_{1}\right)=0
$$