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

To determine which system of equations has no solution, we need to check if the equations in each system are inconsistent, meaning they represent parallel lines that never intersect.

1. **First System:**
\[
\begin{align*}
4x - y &= -17 \quad (1) \\
4x + y &= 3 \quad (2)
\end{align*}
\]
Adding equations \( (1) \) and \( (2) \):
\[
(4x - y) + (4x + y) = -17 + 3 \implies 8x = -14 \implies x = -\frac{14}{8} = -\frac{7}{4}
\]
Substitute \( x = -\frac{7}{4} \) back into either equation to solve for \( y \):
\[
4(-\frac{7}{4}) - y = -17 \implies -7 - y = -17 \implies y = 10
\]
This system has a solution.

2. **Second System:**
\[
\begin{align*}
4x - y &= 17 \quad (1) \\
4x + y &= 3 \quad (2)
\end{align*}
\]
Adding equations \( (1) \) and \( (2) \):
\[
(4x - y) + (4x + y) = 17 + 3 \implies 8x = 20 \implies x = 2.5
\]
Substitute \( x = 2.5 \) back into either equation to solve for \( y \):
Equation (1):
\[
4(2.5) - y = 17 \implies 10 - y = 17 \implies y = -7
\]
This system has a solution.

3. **Third System:**
\[
\begin{align*}
4x + y &= 17 \quad (1) \\
4x - y &= 3 \quad (2)
\end{align*}
\]
Adding equations \( (1) + (2) \):
\[
(4x + y) + (4x - y) = 17 + 3 \implies 8x = 20 \implies x = 2.5
\]
Substitute \( x = 2.5 \):
\[
4(2.5) + y = 17 \implies 10 + y = 17 \implies y = 7
\]
This system has a solution.

4. **Fourth System:**
\[
\begin{align*}
4x - y &= 17 \quad (1) \\
4x - y &= 3 \quad (2)
\end{align*}
\]
Since both equations are equivalent (\( 4x - y \) is the same in both equations), they yield:
\[
17 \neq 3
\]
This system is inconsistent and has no solution.

Therefore, the system that has no solution is:
\[
\{4x - y = 17 \\ 4x - y = 3\}
\]