We are given the system of linear equations:

1. $3x + 2y = 8$
2. $5x + 2y = 12$

To solve this system, we can use the elimination method. Let's eliminate $y$ by subtracting the first equation from the second equation:

$(5x + 2y) - (3x + 2y) = 12 - 8$

Simplifying:

$5x - 3x + 2y - 2y = 4$

$2x = 4$

Solving for $x$:

$x = \frac{4}{2} = 2$

Now substitute $x = 2$ into either of the original equations. Let's use the first equation:

$3x + 2y = 8$

Substitute $x = 2$:

$3(2) + 2y = 8$

$6 + 2y = 8$

Now solve for $y$:

$2y = 8 - 6$

$2y = 2$

$y = \frac{2}{2} = 1$

Thus, the solution is $(x, y) = (2, 1)$.

Answer: B. (2, 1)

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Do you want a more detailed explanation of the elimination method or have any other questions? Here are some related questions to explore:

1. How would you solve this system using substitution instead of elimination?
2. What happens if we have three variables instead of two in a system of equations?
3. Can this system be solved using matrices? How?
4. What are some special types of systems of equations (e.g., dependent, inconsistent)?
5. How can you verify the solution by substituting back into both equations?

Tip: The elimination method works best when the coefficients of one variable are the same or easily manipulated to be the same across the equations.