Let's solve the system of equations provided:

1. $2x + y = 7$
2. $x - y = 2$

We will solve this algebraically rather than graphically for efficiency.

Step 1: Solve the second equation for $y$

$x - y = 2 \implies y = x - 2$

Step 2: Substitute $y = x - 2$ into the first equation

$2x + (x - 2) = 7$ Simplifying: $2x + x - 2 = 7$ $3x - 2 = 7$ $3x = 9 \implies x = 3$

Step 3: Solve for $y$

Substitute $x = 3$ into $y = x - 2$: $y = 3 - 2 = 1$

Solution:

The solution is $(x, y) = (3, 1)$.

Therefore, the correct answer is b. (3, 1).

Would you like more details or have any questions?

Here are some related questions to expand on this:

1. What method can be used to solve systems of equations algebraically besides substitution?
2. How can you graphically determine the solution to a system of equations?
3. What is the elimination method in solving systems of equations?
4. What is the geometric interpretation of a solution to a system of two linear equations?
5. How do you know when a system of equations has no solution?

Tip: When solving systems of equations graphically, the solution is the point where the lines intersect.