Question Show Examples 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 \(\boxed{\text{Infinitely Many Solutions}}\).