https://file.aiquickdraw.com/mathbot/file/17296187974613glbqhtg.jpg

The system of equations given in the image is:

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

We need to solve this system to find the values of \(x\) and \(y\).

### Step 1: Solve one equation for \(x\) or \(y\)
Let's start with the second equation:
\[
4y = -2 + x
\]
Rearrange it to express \(x\) in terms of \(y\):
\[
x = 4y + 2
\]

### Step 2: Substitute \(x\) into the first equation
Now substitute \(x = 4y + 2\) into the first equation:
\[
-2(4y + 2) + y = 3
\]
Simplify:
\[
-8y - 4 + y = 3
\]
\[
-7y - 4 = 3
\]
Add 4 to both sides:
\[
-7y = 7
\]
Divide by \(-7\):
\[
y = -1
\]

### Step 3: Substitute \(y = -1\) into the equation for \(x\)
Now substitute \(y = -1\) into \(x = 4y + 2\):
\[
x = 4(-1) + 2 = -4 + 2 = -2
\]

### Solution:
The solution to the system of equations is \(x = -2\) and \(y = -1\), which corresponds to option **A** \((-2, -1)\).

Would you like further details or have any other questions?

Here are 5 related questions to expand on this:
1. How do you verify the solution to a system of equations?
2. Can this system of equations be solved using the elimination method?
3. What is the graphical interpretation of the solution to a system of equations?
4. How would the solution change if the coefficients were different?
5. How do you solve systems of equations using matrices?

**Tip:** Always check your solution by plugging the values back into the original equations to ensure they satisfy both.

Solve the system of equations: -2x + y = 3 and 4y = -2 + x.

Learn how to solve the system of linear equations -2x + y = 3 and 4y = -2 + x using substitution. This step-by-step solution covers essential algebraic techniques, making it perfect for Grades 9-11 students.

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