Question
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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\[
\begin{aligned}
6 x+5 y & =-2 \\
-30 x-25 y & =10
\end{aligned}
\]

Answer
Infinitely Many Solutions
One Solution
Euthenit Amser
No Solutions

Step 1 ：The given system of equations is a linear system. To determine if the system has no solutions, infinitely many solutions or exactly one solution, we can use the method of elimination or substitution.

Step 2 ：However, in this case, it is easier to observe that the second equation is just the first equation multiplied by -5.

Step 3 ：This means that the two equations are dependent and represent the same line.

Step 4 ：Therefore, the system has infinitely many solutions.

Step 5 ：The solution set indicates that for any value of y, there is a corresponding value of x that makes both equations true.

Step 6 ：This confirms our initial thought that the system of equations has infinitely many solutions.

Step 7 ：Final Answer: The system of equations has \(\boxed{\text{Infinitely Many Solutions}}\).