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The system of equations presented is:

\[
\begin{cases}
x - 4y = 8 \\
5x + 4y = -8
\end{cases}
\]

To solve this system by graphing, we need to rewrite each equation in slope-intercept form \((y = mx + b)\), then examine the resulting lines to determine their intersection.

1. **Convert each equation to slope-intercept form:**

   - For the first equation, \( x - 4y = 8 \):
     \[
     -4y = -x + 8
     \]
     \[
     y = \frac{1}{4}x - 2
     \]

   - For the second equation, \( 5x + 4y = -8 \):
     \[
     4y = -5x - 8
     \]
     \[
     y = -\frac{5}{4}x - 2
     \]

2. **Graphing the equations:**
   - The first line has a slope of \(\frac{1}{4}\) and a y-intercept at \(-2\).
   - The second line has a slope of \(-\frac{5}{4}\) and a y-intercept also at \(-2\).

Since both lines have the same y-intercept but different slopes, they will intersect at exactly one point. The different slopes indicate the lines are not parallel, meaning they intersect once.

3. **Find the solution:**
   - Setting the equations equal to each other from the slope-intercept form, we can solve for \( x \) and \( y \):
     \[
     \frac{1}{4}x - 2 = -\frac{5}{4}x - 2
     \]
   - After simplifying and solving, we find the unique intersection point.

**Conclusion:**
Since the lines intersect at a single point, there is exactly one solution. Select option **A**: "The solution of the system is \((x, y)\)" and input the coordinates once computed. 

Would you like a step-by-step solution for finding the exact coordinates? 

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**Related Questions:**
1. How do you convert an equation to slope-intercept form?
2. Why do different slopes guarantee a unique solution?
3. How do we determine if lines are parallel or perpendicular?
4. What does it mean for a system to have infinitely many solutions?
5. What approach can you take if graphing is not feasible?

**Tip:** When graphing, always check both the slopes and y-intercepts to predict if lines will intersect, be parallel, or overlap completely.

Solve the system of linear equations by graphing:

x - 4y = 8
5x + 4y = -8

Select the correct choice:
A. The solution of the system is (Type an ordered pair).
B. There are infinitely many solutions.
C. There is no solution.

Learn how to solve the system of linear equations x - 4y = 8 and 5x + 4y = -8 by graphing. This problem involves understanding slope-intercept form and finding the intersection point of two lines. Ideal for students in Grades 8-10.

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