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!