To determine which systems of equations have no solution, we need to analyze each system one-by-one. Let's verify:
1. System 1:
[tex]\[
\begin{aligned}
x + 4y & = 23 \\
-3x - 12y & = -1
\end{aligned}
\][/tex]
After examination, this system has no solution.
2. System 2:
[tex]\[
\begin{aligned}
2x + 4y & = 22 \\
-x - 2y & = 11
\end{aligned}
\][/tex]
After examination, this system has no solution.
3. System 3:
[tex]\[
\begin{aligned}
2x + y & = 17 \\
-4x - 2y & = -34
\end{aligned}
\][/tex]
After examination, this system has a solution.
4. System 4:
[tex]\[
\begin{aligned}
3y & = 10 - x \\
2x + 6y & = 7
\end{aligned}
\][/tex]
After examination, this system has no solution.
5. System 5:
[tex]\[
\begin{aligned}
2x + y & = 15 \\
x & = 15 - 2y
\end{aligned}
\][/tex]
After examination, this system has a solution.
6. System 6:
[tex]\[
\begin{aligned}
y & = 13 - 2x \\
4x - y & = -1
\end{aligned}
\][/tex]
After examination, this system has a solution.
Based on this detailed analysis, the systems of equations that have no solution are:
1. System 1:
[tex]\[
\begin{aligned}
x + 4y & = 23 \\
-3x - 12y & = -1
\end{aligned}
\][/tex]
2. System 2:
[tex]\[
\begin{aligned}
2x + 4y & = 22 \\
-x - 2y & = 11
\end{aligned}
\][/tex]
4. System 4:
[tex]\[
\begin{aligned}
3y & = 10 - x \\
2x + 6y & = 7
\end{aligned}
\][/tex]
