Alright, let's carefully match each system of equations to its corresponding solution based on the given results.
1. System of Equations:
[tex]\[
\begin{aligned}
2 x + y & = 12 \\
x & = 9 - 2 y
\end{aligned}
\][/tex]
After analyzing the solutions provided, none of the values [tex]\( (x, y) = (2, 7), (5, 2), (3, 5), (7, 3) \)[/tex] satisfy both equations in this system.
Therefore, for this system, the solution is:
[tex]\[
\boxed{\text{None}}
\][/tex]
2. System of Equations:
[tex]\[
\begin{aligned}
x + 2 y & = 9 \\
2 x + 4 y & = 20
\end{aligned}
\][/tex]
By comparing the solutions, none of the values [tex]\( (x, y) = (2, 7), (5, 2), (3, 5), (7, 3) \)[/tex] satisfy these equations either.
Therefore, for this system, the solution is:
[tex]\[
\boxed{\text{None}}
\][/tex]
3. System of Equations:
[tex]\[
\begin{aligned}
x + 3 y & = 16 \\
2 x - y & = 11
\end{aligned}
\][/tex]
Here, the solution [tex]\( (x, y) = (7, 3) \)[/tex] satisfies both equations:
[tex]\[
7 + 3 \cdot 3 = 16 \\
2 \cdot 7 - 3 = 11
\][/tex]
Thus, the solution for this system is:
[tex]\[
\boxed{(7, 3)}
\][/tex]
To summarize the matches:
1. [tex]\[
\begin{aligned}
2 x + y & = 12 \\
x & = 9 - 2 y
\end{aligned}
\][/tex]
with [tex]\( \boxed{\text{None}} \)[/tex]
2. [tex]\[
\begin{aligned}
x + 2 y & = 9 \\
2 x + 4 y & = 20
\end{aligned}
\][/tex]
with [tex]\( \boxed{\text{None}} \)[/tex]
3. [tex]\[
\begin{aligned}
x + 3 y & = 16 \\
2 x - y & = 11
\end{aligned}
\][/tex]
with [tex]\( \boxed{(7, 3)} \)[/tex]
