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The system of equations given is:

1. \( 4x - 3y = 12 \)
2. \( 2x + y = -4 \)

To solve this by graphing, we will first convert both equations into slope-intercept form (i.e., \( y = mx + b \)).

### Step 1: Convert both equations to slope-intercept form.

#### For the first equation \( 4x - 3y = 12 \):
\[
-3y = -4x + 12 \quad \text{(subtracting \(4x\) from both sides)}
\]
\[
y = \frac{4x - 12}{3} \quad \text{(dividing by -3)}
\]
This simplifies to:
\[
y = \frac{4}{3}x - 4
\]
The equation for the first line is:
\[
y = \frac{4}{3}x - 4
\]

#### For the second equation \( 2x + y = -4 \):
Subtract \( 2x \) from both sides:
\[
y = -2x - 4
\]
The equation for the second line is:
\[
y = -2x - 4
\]

### Step 2: Graph both lines.

- The first equation \( y = \frac{4}{3}x - 4 \) has a slope of \( \frac{4}{3} \) and a y-intercept at \( -4 \).
- The second equation \( y = -2x - 4 \) has a slope of \( -2 \) and a y-intercept also at \( -4 \).

Since both lines share the same y-intercept at \( -4 \), plot that point. Then use the slopes to plot additional points for each line.

### Step 3: Find the intersection point.

From the equations, we can see that both lines intersect at the point \( (0, -4) \). This is the solution to the system of equations.

### Solution:
The solution to the system is \( (0, -4) \).

Would you like more details or have any questions?

### 5 Related Questions:
1. How do you find the slope of a line from its equation?
2. What are the steps to convert any linear equation into slope-intercept form?
3. How do parallel lines differ in terms of their slopes?
4. What are some other methods to solve systems of equations besides graphing?
5. How can you check if a solution is correct without graphing?

### Tip:
When graphing a system of equations, always verify the solution by substituting it back into both original equations to ensure it satisfies both.

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

Learn how to solve the system of linear equations 4x - 3y = 12 and 2x + y = -4 by graphing. This guide walks through converting equations to slope-intercept form and finding the point of intersection. Suitable for students in Grades 8-10.

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