https://file.aiquickdraw.com/mathbot/file/1729701098540nq0prr8u.jpg

The image contains a system of linear equations:

\[
\begin{aligned}
2x + 4y &= 8 \\
3x - 4y &= 12
\end{aligned}
\]

You are asked to solve the system by graphing and select the solution.

### Steps to solve the system by graphing:
1. **Rewrite both equations in slope-intercept form** (y = mx + b).
   
   For the first equation:
   \[
   2x + 4y = 8 \implies 4y = -2x + 8 \implies y = -\frac{1}{2}x + 2
   \]
   The slope is \(-\frac{1}{2}\) and the y-intercept is 2.

   For the second equation:
   \[
   3x - 4y = 12 \implies -4y = -3x + 12 \implies y = \frac{3}{4}x - 3
   \]
   The slope is \(\frac{3}{4}\) and the y-intercept is -3.

2. **Plot both equations** on the graph using their slopes and intercepts:
   - For \(y = -\frac{1}{2}x + 2\), start at (0, 2) and use the slope \(-\frac{1}{2}\), meaning go down 1 unit and right 2 units.
   - For \(y = \frac{3}{4}x - 3\), start at (0, -3) and use the slope \(\frac{3}{4}\), meaning go up 3 units and right 4 units.

3. **Find the intersection point**, which represents the solution of the system.

After plotting both lines, you should find that the two lines intersect at a specific point, which will be the solution to the system of equations. 

Would you like a detailed graph or any further clarification? Here are five related questions you might explore:

1. How do you solve systems of equations algebraically (e.g., by substitution or elimination)?
2. How do slopes and intercepts affect the shape and position of a line in a graph?
3. Can two lines in a system of equations be parallel? If so, what does that mean for the solution?
4. How do you determine if a system of equations has infinitely many solutions?
5. What methods can be used to solve nonlinear systems of equations?

**Tip:** When graphing a system of linear equations, always double-check that you have plotted enough points accurately for each line to ensure their intersection (if any) is clear.

Solve the system by graphing: 2x + 4y = 8 and 3x - 4y = 12.

Learn how to solve the system of linear equations 2x + 4y = 8 and 3x - 4y = 12 by graphing. This problem demonstrates key concepts such as slope-intercept form and the intersection of lines, suitable for Grade 8-10 students.

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