The problem asks to solve the system of equations using the elimination method:

1. $3x + y = 4$
2. $-3x + y = -2$

Step 1: Add the equations to eliminate $x$

$(3x + y) + (-3x + y) = 4 + (-2)$ This simplifies to: $y + y = 2 \quad \text{or} \quad 2y = 2$ $y = 1$

Step 2: Substitute $y = 1$ into one of the original equations. Let's use the first equation:

$3x + 1 = 4$ $3x = 3 \quad \text{so} \quad x = 1$

Solution:

The solution to the system of equations is $x = 1$ and $y = 1$, or the point $(1, 1)$.

Thus, the correct answer is $(1, 1)$.

Would you like more details on this method or have any further questions?

Here are 5 related questions you can explore:

1. How do you use substitution instead of elimination to solve this system?
2. Can all systems of linear equations be solved using the elimination method?
3. What happens if both variables cancel out in elimination?
4. How do you handle systems of equations with three variables using elimination?
5. What is the geometric interpretation of solving a system of two linear equations?

Tip: When using elimination, aim to cancel one variable by adding or subtracting equations. If necessary, multiply one or both equations by a constant to align coefficients.