Let's match the given systems of equations to their solutions based on the steps and results provided:
1. First System:
[tex]\[
\begin{aligned}
2x + y &= 12 \\
x &= 9 - 2y \\
\end{aligned}
\][/tex]
The solution to this system is:
[tex]\[
(x, y) = (5, 2)
\][/tex]
So, the pair is:
[tex]\[
\left( x = 5, y = 2 \right)
\][/tex]
2. Second System:
[tex]\[
\begin{aligned}
y &= 10 + x \\
-3x + 3y &= 30 \\
\end{aligned}
\][/tex]
The solution to this system is:
[tex]\[
x = y - 10
\][/tex]
This implies that there isn't a specific numeric pair for [tex]\(x\)[/tex] and [tex]\(y\)[/tex], thus it falls under the solution: [tex]\( \left( x = y - 10 \right) \)[/tex]. The solution doesn't match a specific box in your query.
3. Third System:
[tex]\[
\begin{aligned}
x + 2y &= 9 \\
2x + 4y &= 20 \\
\end{aligned}
\][/tex]
The solution for this system of equations is an empty set:
[tex]\[
\left( \text{no solution} \right)
\][/tex]
Since this system does not have a solution, it does not match any of the numeric pairs.
4. Fourth System:
[tex]\[
\begin{aligned}
2x + y &= 11 \\
x - 2y &= -7 \\
\end{aligned}
\][/tex]
The solution to this system is:
[tex]\[
(x, y) = (3, 5)
\][/tex]
So, the pair is:
[tex]\[
\left( x = 3, y = 5 \right)
\][/tex]
Therefore, the correct pairs to complete the boxes are:
1. First Box: [tex]\( \left( x = 5, y = 2 \right) \)[/tex]
2. Second Box: [tex]\(\text{no solution} \implies \text{this needs to be left blank}\)[/tex]
3. Third Box: [tex]\(\text{does not fit any specific solution}\)[/tex]
4. Fourth Box: [tex]\( \left( x = 3, y = 5 \right) \)[/tex]
