To solve the given task, we need to determine the number of solutions for each system of equations and then arrange the systems in order from least to greatest based on the number of solutions.
### System 1:
[tex]\[
\begin{array}{r}
-5 x+y=10 \\
-25 x+5 y=50
\end{array}
\][/tex]
This system has 1 solution.
### System 2:
[tex]\[
\begin{array}{r}
3 x-7 y=9 \\
-4 x+5 y=1
\end{array}
\][/tex]
This system has 2 solutions.
### System 3:
[tex]\[
\begin{array}{l}
y=6 x-2 \\
y=6 x-4
\end{array}
\][/tex]
This system has 0 solutions.
### Ordering the Systems
1. The system with 0 solutions:
[tex]\[
\begin{array}{l}
y=6 x-2 \\
y=6 x-4
\end{array}
\][/tex]
2. The system with 1 solution:
[tex]\[
\begin{array}{r}
-5 x+y=10 \\
-25 x+5 y=50
\end{array}
\][/tex]
3. The system with 2 solutions:
[tex]\[
\begin{array}{r}
3 x-7 y=9 \\
-4 x+5 y=1
\end{array}
\][/tex]
Therefore, the order of systems from least to greatest based on the number of solutions is:
[tex]\[
y=6 x-2 \\
y=6 x-4
\][/tex]
[tex]\[
-5 x + y = 10 \\
-25 x + 5 y = 50
\][/tex]
[tex]\[
3 x - 7 y = 9 \\
-4 x + 5 y = 1
\][/tex]
