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The problem is asking you to solve the following system of linear equations by graphing:

\[
\begin{aligned}
4x + 2y &= -6 \\
-5x + y &= 4
\end{aligned}
\]

To find the solution by graphing, let's solve each equation for \(y\) and then graph them.

### Step 1: Solve each equation for \(y\)

1. **First equation:** \(4x + 2y = -6\)

   Subtract \(4x\) from both sides:
   \[
   2y = -4x - 6
   \]
   
   Now, divide by 2:
   \[
   y = -2x - 3
   \]

2. **Second equation:** \(-5x + y = 4\)

   Add \(5x\) to both sides:
   \[
   y = 5x + 4
   \]

### Step 2: Graph both equations

1. The first equation \(y = -2x - 3\) is a straight line with a slope of \(-2\) and a y-intercept of \(-3\).
2. The second equation \(y = 5x + 4\) is a straight line with a slope of \(5\) and a y-intercept of \(4\).

When you graph these two lines, they will intersect at one point, which is the solution to the system of equations.

### Step 3: Solve by substitution or graphing

To find the solution algebraically, set the two equations for \(y\) equal to each other:

\[
-2x - 3 = 5x + 4
\]

Solve for \(x\):

\[
-2x - 5x = 4 + 3 \implies -7x = 7 \implies x = -1
\]

Now substitute \(x = -1\) into one of the original equations (e.g., \(y = 5x + 4\)):

\[
y = 5(-1) + 4 = -5 + 4 = -1
\]

Thus, the solution is the ordered pair \((-1, -1)\).

### Conclusion

The solution to the system of equations is \((-1, -1)\). You should select option **A** and input \((-1, -1)\) as the ordered pair.

---

Would you like more details or have any other questions?

### Related Questions:
1. How do you graph a line using its slope and y-intercept?
2. What is the method for solving a system of equations by substitution?
3. Can a system of linear equations have infinitely many solutions?
4. How can you verify the solution to a system of equations?
5. What are other methods for solving systems of equations (besides graphing)?

#### Tip:
When solving systems of equations graphically, it's helpful to use precise points (like intercepts) to make the graph accurate.

Solve the system of equations by graphing: 4x + 2y = -6 and -5x + y = 4.

Learn how to solve the system of equations 4x + 2y = -6 and -5x + y = 4 by graphing. This problem covers key algebra concepts, including solving linear equations and finding the intersection of two lines. Suitable for students in Grades 8-10.

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