We can solve this system of equations using either substitution or elimination. Let's use the elimination method to find the values of $x$ and $y$.

The system of equations:

$1) \quad x + 3y = 7$ $2) \quad 2x + 3y = 11$

Step 1: Eliminate one variable

We can eliminate the $3y$ term by subtracting equation (1) from equation (2):

$(2x + 3y) - (x + 3y) = 11 - 7$ This simplifies to: $x = 4$

Step 2: Substitute the value of $x = 4$ back into one of the original equations.

Using equation (1): $4 + 3y = 7$ Solve for $y$: $3y = 7 - 4$ $3y = 3$ $y = 1$

Final solution:

$x = 4, \quad y = 1$

Would you like more details on how we arrived at the solution, or do you have any other questions?

Here are 5 related questions you might find interesting:

1. How would you solve the system using the substitution method?
2. What happens if the system has no solution or an infinite number of solutions?
3. How would this system look in matrix form?
4. Can you solve a system with three variables using elimination?
5. What is the graphical interpretation of solving a system of equations?

Tip: The elimination method works best when coefficients of one variable are already equal in both equations, as we did with the $3y$ terms here!