Quostion 5
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What is the solution to this systems of equations.

Select Two that apply
A. The systems of equations create one solution.
B. The slopes are different but, the -intercepts are the same.
C. The systems of equations create infinitely many solutions
D. The slopes are the same but, the -intercepts are different.
E. The systems of equations create no solution.

Ask by Pearson Weber. in the United States

Jan 24,2025

Question

Quostion 5
pause
zoom

What is the solution to this systems of equations.

Select Two that apply
A. The systems of equations create one solution.
B. The slopes are different but, the -intercepts are the same.
C. The systems of equations create infinitely many solutions
D. The slopes are the same but, the -intercepts are different.
E. The systems of equations create no solution.

Ask by Pearson Weber. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

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.
The correct options are D and E. D. The slopes are the same but, the $$ y $$-intercepts are different. E. The systems of equations create no solution.

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