There are two numbers, \( x \) and \( y \), expressed in base 10. The sum of the two numbers is 12, and the difference between the two numbers is 4. Solve the system of equations using the elimination method to find the values of \( x \) and \( y \). Additionally, determine whether both \( x \) and \( y \) are prime numbers. Let's think step by step and output the final answer within \boxed{}.
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