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You provided a system of equations that needs to be graphed and solved. The system is:

\[
\begin{cases}
2x + y = -5 \\
y = -\frac{1}{4}x + 2
\end{cases}
\]

### Steps to Solve:

1. **Rewrite the first equation** to express \( y \) in terms of \( x \):
   
   \[
   y = -2x - 5
   \]

   So, the system becomes:
   \[
   \begin{cases}
   y = -2x - 5 \\
   y = -\frac{1}{4}x + 2
   \end{cases}
   \]

2. **Graph both equations**:
   - The first equation \( y = -2x - 5 \) is a line with a slope of \( -2 \) and a y-intercept at \( (0, -5) \).
   - The second equation \( y = -\frac{1}{4}x + 2 \) is a line with a slope of \( -\frac{1}{4} \) and a y-intercept at \( (0, 2) \).

3. **Find the intersection**:
   The solution to the system is where the two lines intersect. We can set the two equations equal to each other:
   \[
   -2x - 5 = -\frac{1}{4}x + 2
   \]

4. **Solve algebraically**:
   Multiply through by 4 to eliminate the fraction:
   \[
   4(-2x - 5) = -x + 8
   \]
   \[
   -8x - 20 = -x + 8
   \]
   Add \( 8x \) to both sides:
   \[
   -20 = 7x + 8
   \]
   Subtract 8 from both sides:
   \[
   -28 = 7x
   \]
   Divide by 7:
   \[
   x = -4
   \]

5. **Find \( y \)**:
   Substitute \( x = -4 \) into one of the original equations (let's use \( y = -2x - 5 \)):
   \[
   y = -2(-4) - 5 = 8 - 5 = 3
   \]

The solution is \( (x, y) = (-4, 3) \).

Would you like a graph of this system as well?

### Follow-up questions:
1. How do we find the slope of a linear equation?
2. What is the general form of a linear equation in slope-intercept form?
3. What does the slope of a line represent in a graph?
4. How do you interpret the solution of a system of linear equations?
5. How would you check the solution by substituting the values back into the original equations?

**Tip:** Always verify your solution by substituting the values back into both original equations to ensure they hold true.

Graph the system below and write its solution: 
2x + y = -5 
 y = -(1/4)x + 2

Learn how to graph and solve the system of linear equations 2x + y = -5 and y = -(1/4)x + 2. This problem covers key concepts like slope-intercept form, graphing lines, and finding the intersection of two equations. Suitable for students in Grades 8-10.

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