You are given the two equations
\[
\left.\begin{array}{c}
a y+x+b=0 \\
-5 y-3 x+7=0
\end{array}\right\}
\]
where \( a \) and \( b \) are constants.
For each of the following statements, decide if it is always, sometimes or never true.
For those which you decide are "sometimes" true, give examples of values for \( a \) and \( b \) which make the statement true.
1. The system (*) has no solutions.
(Clear my choice)
If you think "sometimes" then give an example: \( a= \) □ \( b= \) □
2. The system (*) has precisely one solution. (Clear my choice)
If you think "sometimes" then give an example: \( a= \) □ \( b= \) □
3. The system (*) has precisely two solutions. (Clear my choice)
If you think "sometimes" then give an example: \( a= \) □ \( b= \) □
4. The system (*) has infinitely many solutions. □ (Clear my choice)
If you think "sometimes" then give an example: \( a= \) □ \( b= \) □