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

To determine which system of linear equations has no solution, we look for systems that represent parallel lines. Parallel lines have the same slope but different y-intercepts.

Let's analyze each system:

1. **System:**
- \(4x - y = -17\)
- \(4x + y = 3\)

- Convert to slope-intercept form \(y = mx + b\):
- First equation: \(y = 4x + 17\) (slope \(m = 4\))
- Second equation: \(y = -4x + 3\) (slope \(m = -4\))
- **Conclusion:** Different slopes → has a solution (intersecting lines).

2. **System:**
- \(4x - y = 17\)
- \(4x + y = 3\)

- Convert to slope-intercept form:
- First equation: \(y = 4x - 17\) (slope \(m = 4\))
- Second equation: \(y = -4x + 3\) (slope \(m = -4\))
- **Conclusion:** Different slopes → has a solution (intersecting lines).

3. **System:**
- \(4x + y = 17\)
- \(4x - y = 3\)

- Convert to slope-intercept form:
- First equation: \(y = -4x + 17\) (slope \(m = -4\))
- Second equation: \(y = 4x - 3\) (slope \(m = 4\))
- **Conclusion:** Different slopes → has a solution (intersecting lines).

4. **System:**
- \(4x - y = 17\)
- \(4x - y = 3\)

- The first equation can be rewritten as \(y = 4x - 17\) and the second equation as \(y = 4x - 3\). Both equations have the same slope (\(m = 4\)) but different y-intercepts.
- **Conclusion:** The lines are parallel and never intersect → this system has no solution.

From the analysis, the system of linear equations that has no solution is:

\[
\{4x - y = 17, \, 4x - y = 3\}
\]