1. Two cars started from the same place but in opposite directions. At the moment when their distance was $18 \mathrm{~km}$, one car had traveled $3 \mathrm{~km}$ less than twice the distance of the other. Determine the distance each car had traveled by that moment.
Solution. Let $x$ and $y$ be the distances traveled by the cars. From the condition of the problem: $x+y=9$ and $x=2 y-3$. The solution to this system of equations is $x=11$, $y=7$. Therefore, one car traveled $11 \mathrm{~km}$, and the other $7 \mathrm{~km}$.