Answer:

D) The value cannot be determined from the information given.

• If 3x-y=12, what is the value of 8x2y?
• This problem is ambiguous.
• The given equation has rational solutions because gcd( 3 , 1 ) = 1|12.
• 3x−y=12⟹y=3x−12.
• Letting x=t , where t is a constant, get the parametric equations
• x=t, y=3t−12.
• What is 8x2y? Here is where the ambiguity comes in. It is either 16xy or it is 8x2y.
• x=t, y=3t−12
• ⟹16xy=16t(3t−12)
• =48t2−192t,
• 8x2y=8t2(3t−12)
• =24t3−96t2,
• t an integer.
• So there are many answers for this problem. Choose values of t to get some.
• If you don't want to use the parameter t, then have that
• 16xy=48x2−192x and
• 8x2y=24x3−96x2.
• However, these look complicated.

Step-by-step explanation:

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