https://file.aiquickdraw.com/mathbot/file/17297945330664pazbb97.jpg

We are tasked with solving the system of equations shown in the image:

\[
3x - y = 7 \quad \text{(Equation 1)}
\]
\[
2x + y = 3 \quad \text{(Equation 2)}
\]

### Step 1: Add the equations
We can eliminate \( y \) by adding both equations together:

\[
(3x - y) + (2x + y) = 7 + 3
\]
This simplifies to:
\[
5x = 10
\]

### Step 2: Solve for \( x \)
\[
x = \frac{10}{5} = 2
\]

### Step 3: Substitute \( x = 2 \) into one of the original equations
Let's substitute it into Equation 1:
\[
3(2) - y = 7
\]
\[
6 - y = 7
\]
\[
-y = 1 \quad \Rightarrow \quad y = -1
\]

### Solution:
The solution to the system is \( (x, y) = (2, -1) \).

Thus, the correct answer is **(2, -1)**.

Would you like more details on any part of the process? 

Here are some related questions you might find helpful:
1. What are some methods to solve a system of equations?
2. How does the substitution method differ from elimination?
3. Can all systems of linear equations be solved by elimination?
4. What are some cases where a system of equations has no solution?
5. How can you graphically represent the solution to this system?

**Tip**: When solving systems of equations, the elimination method is often quicker when the coefficients of one variable are already opposites, like in this example!

Solve the system of equations: 3x - y = 7, 2x + y = 3

Learn how to solve the system of linear equations 3x - y = 7 and 2x + y = 3 using the elimination method. This problem covers fundamental algebraic concepts and is ideal for students in Grades 8-10.

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