Quostion 5 pause zoom What is the solution to this systems of equations. \[ \begin{array}{l} y=2 x+4 \\ y=2 x+1 \end{array} \] Select Two that apply A. The systems of equations create one solution. B. The slopes are different but, the \( y \)-intercepts are the same. C. The systems of equations create infinitely many solutions D. The slopes are the same but, the \( y \)-intercepts are different. E. The systems of equations create no solution.

Let's analyze the given system of equations: \[ \begin{cases} y = 2x + 4 \\ y = 2x + 1 \end{cases} \] 1. **Slope Comparison**: - Both equations have the same slope (\( m = 2 \)). 2. **Y-Intercept Comparison**: - The first equation has a y-intercept of \( 4 \). - The second equation has a y-intercept of \( 1 \). Since both lines have the **same slope** but **different y-intercepts**, they are **parallel** and will **never intersect**. This means: - There is **no solution** to the system because there is no point \((x, y)\) that satisfies both equations simultaneously. **Evaluating the Options:** - **A. The systems of equations create one solution.** - **Incorrect**. Parallel lines do not intersect, so there is no solution. - **B. The slopes are different but, the \( y \)-intercepts are the same.** - **Incorrect**. The slopes are the **same**, and the y-intercepts are **different**. - **C. The systems of equations create infinitely many solutions.** - **Incorrect**. This would only be true if both equations were identical. - **D. The slopes are the same but, the \( y \)-intercepts are different.** - **Correct**. This accurately describes the given system. - **E. The systems of equations create no solution.** - **Correct**. Parallel lines do not intersect, resulting in no solution. **Therefore, the correct options are D and E.** **Answer:** D. The slopes are the same but, the \( y \)-intercepts are different. E. The systems of equations create no solution.