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

To determine which system of linear equations has no solution, we need to check for parallel lines, which occurs when the equations have the same slope but different y-intercepts.

Let's analyze each system:

1. **System 1:**
\[
\begin{cases}
4x + y = 17 \\
4x - y = 3
\end{cases}
\]
- Rearranging the equations:
- \(y = -4x + 17\) (first equation)
- \(y = 4x - 3\) (second equation)
- The slopes are \(-4\) and \(4\) (not parallel, so this system has a solution).

2. **System 2:**
\[
\begin{cases}
4x - y = 17 \\
4x - y = 3
\end{cases}
\]
- Both equations are identical in form, the first can be represented as \(y = 4x - 17\) and the second as \(y = 4x - 3\).
- They have the same slope (\(4\)) but different y-intercepts (17 vs. 3), so these lines are parallel (no solution).

3. **System 3:**
\[
\begin{cases}
4x - y = 17 \\
4x + y = 3
\end{cases}
\]
- Rearranged forms:
- \(y = 4x - 17\)
- \(y = -4x + 3\)
- The slopes are \(4\) and \(-4\) (not parallel), so this system has a solution.

4. **System 4:**
\[
\begin{cases}
4x - y = -17 \\
4x + y = 3
\end{cases}
\]
- Rearranged forms:
- \(y = 4x + 17\)
- \(y = -4x + 3\)
- The slopes are \(4\) and \(-4\) (not parallel), so this system has a solution.

The only system with no solution is **System 2**:

\[
\begin{cases}
4x - y = 17 \\
4x - y = 3
\end{cases}
\]