Which of the following systems of linear equations has no solution?(1 point)

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:
\[
\{4x−y=17, \, 4x−y=3\}
\]