The system of equations given is:

$y = 3x + 1$ $y = 2x + 2$

We can solve this system by substitution or elimination. Let's use the substitution method:

Step 1: Set the two equations equal to each other.

Since both equations are equal to $y$, we can equate the right-hand sides:

$3x + 1 = 2x + 2$

Step 2: Solve for $x$.

Subtract $2x$ from both sides:

$x + 1 = 2$

Now subtract 1 from both sides:

$x = 1$

Step 3: Substitute $x = 1$ into one of the original equations to find $y$.

Substitute into the first equation:

$y = 3(1) + 1 = 3 + 1 = 4$

So, the solution to the system is $x = 1$ and $y = 4$, or the point $(1, 4)$.

The correct answer is the fourth option: $(1, 4)$.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. What is the elimination method for solving systems of equations?
2. Can a system of linear equations have no solution?
3. How do you graphically interpret the solution to a system of linear equations?
4. What happens when both equations in a system represent the same line?
5. How do you solve systems of equations with more than two variables?

Tip: When solving a system of equations, always double-check your solution by substituting both variables back into the original equations.