https://file.aiquickdraw.com/mathbot/file/1727485389417hwrtwjbp.jpg

The system of linear equations provided in the image is:

\[
\begin{aligned}
    -6x + 3y &= 12 \\
     8x - 4y &= -16
\end{aligned}
\]

To solve this system by graphing, let's first convert both equations into slope-intercept form (i.e., \( y = mx + b \)):

### Step 1: Rearranging the first equation
\[
-6x + 3y = 12
\]
Solve for \( y \):
\[
3y = 6x + 12
\]
\[
y = 2x + 4
\]
This is the slope-intercept form of the first equation, with a slope of 2 and a y-intercept of 4.

### Step 2: Rearranging the second equation
\[
8x - 4y = -16
\]
Solve for \( y \):
\[
-4y = -8x - 16
\]
\[
y = 2x + 4
\]
This is the slope-intercept form of the second equation, with the same slope of 2 and a y-intercept of 4.

### Step 3: Analyzing the system
Since both equations have the same slope and the same y-intercept, they represent the same line. This means that every point on one line is also on the other line. Therefore, there are infinitely many solutions.

### Conclusion:
The solution to the system of equations is \( \infty \) (infinitely many solutions), so you should enter "∞" or "infinitely many solutions" for the solution.

---

Would you like a more detailed explanation on any part of this process, or help with another question?

Here are some related questions for further practice:
1. How do you identify when two lines are parallel by looking at their slopes?
2. What does it mean when two lines have the same slope and y-intercept?
3. How would the solution change if the slopes were different?
4. Can a system of equations have exactly one solution? If so, when?
5. How can you check a system of equations graphically?

**Tip**: When graphing, if two lines overlap perfectly, it indicates infinitely many solutions. If they are parallel but distinct, the system has no solution.

Solve the system of equations by graphing: -6x + 3y = 12 and 8x - 4y = -16

Solve the system of linear equations -6x + 3y = 12 and 8x - 4y = -16 by graphing. This problem demonstrates how to determine if two lines are identical, resulting in infinitely many solutions. Learn the steps of converting to slope-intercept form and analyzing the system.

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