The problem involves solving a system of linear equations given as:

1. $3x + 2y = 7$
2. $x - y = -1$

Let me solve this step by step.

Step 1: Express $x$ in terms of $y$ from the second equation

From $x - y = -1$, solve for $x$: $x = y - 1$

Step 2: Substitute $x = y - 1$ into the first equation

Substitute $x = y - 1$ into $3x + 2y = 7$: $3(y - 1) + 2y = 7$

Simplify: $3y - 3 + 2y = 7$ $5y - 3 = 7$

Add 3 to both sides: $5y = 10$

Divide by 5: $y = 2$

Step 3: Solve for $x$

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

Final Answer:

The solution is: $x = 1, \, y = 2$

Would you like further clarification or additional details?

Here are 5 related questions to expand your understanding:

1. How do you check if the solution to a system of linear equations is correct?
2. What is the graphical interpretation of solving a system of linear equations?
3. How can substitution be used to solve any system of two linear equations?
4. What are the different methods to solve a system of equations (e.g., elimination, matrix method)?
5. How do systems of equations differ when they have no solution, one solution, or infinitely many solutions?

Tip: Always verify your solution by substituting the values of $x$ and $y$ back into the original equations!