1. If x - 2y = 2 and x ^ 2 + 4xy + 4y ^ 2 = 8, what is the value of xy?
Answer: A
xy equals 1-Feb.
The value of xy is determined to be 1-Feb based on the provided equations and their manipulation.
A) 01-Feb
This option is correct as it represents the value of xy derived from solving the equations given in the question. By substituting and simplifying the first equation into the second, one arrives at this specific value.
B) 1
This option is incorrect because substituting 1 for xy does not satisfy the equations given. When plugged back into the equations, it does not hold true and leads to contradictions.
C) 2
This option is also incorrect; substituting 2 for xy fails to satisfy the original equations. The calculations would not balance out, confirming that this value cannot be correct.
D) 02-May
This option is incorrect as well. The format does not match the expected numerical output for xy, and substituting this value does not yield valid solutions for the equations provided.
Conclusion
The correct answer, 1-Feb, aligns with the results obtained from the equations, confirming its validity. The other options do not satisfy the equations and thus are definitively incorrect, reinforcing the concept of solving simultaneous equations accurately.