To determine which system of linear equations has no solution, we can analyze each option for the possibility of having parallel lines, which implies that they will never intersect.
1. **System 1:**
\[
\begin{align*}
4x - y &= 17 \\
4x - y &= 3
\end{align*}
\]
Here, both equations have the same left-hand side but different right-hand sides, indicating that they represent parallel lines. Thus, this system has no solution.
2. **System 2:**
\[
\begin{align*}
4x - y &= -17 \\
4x + y &= 3
\end{align*}
\]
To determine if this has a solution, we can solve the second equation for \( y \): \( y = 3 - 4x \). Substituting this into the first equation does not yield a contradiction, so this system has a solution.
3. **System 3:**
\[
\begin{align*}
4x - y &= 17 \\
4x + y &= 3
\end{align*}
\]
Again, we can solve the second equation for \( y \): \( y = 3 - 4x \). Substituting into the first equation shows that this system also has a solution.
4. **System 4:**
\[
\begin{align*}
4x + y &= 17 \\
4x - y &= 3
\end{align*}
\]
Here, solving the second equation for \( y \) gives \( y = 4x - 3 \). As before, substituting this into the first equation indicates that this system also has a solution.
**Conclusion:** The only system with no solution is the first one:
\[
\{4x−y=17, \, 4x−y=3\}
\]