题目信息
If N = 
, where T = 
and x = 5 – T, which of the following expresses y in terms of N and T ?
, where T = and x = 5 – T, which of the following expresses y in terms of N and T ?
A:
B:
C:
D:
E:
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已选答案：
正确答案：
A:
Algebra Simplifying algebraic expressions
To eliminate K and x in the first equation (the only equation in which y appears), use the second and third equations to replace K and x with expressions involving only N and T. Then solve for y in terms of N and T.
Alternatively, the algebraic manipulations involved in solving this type of problem as above can often be replaced with numerical computations by assigning values to the variables. The assigned values need to be consistent with all the constraints in the problem, and, for efficiency, the assigned values should be chosen to minimize the numerical computations. Letting K = 10, it follows from T =
and x = 5 – T that T = 2 and x = 3. Using these numerical values, the question can be rephrased as follows.
If N =
, then which of the following expresses y in terms of N ?
Letting y = 1, it follows that N =
= 2. Plugging N = 2 into A, B, C, D, and E above gives, respectively, 1, –1, 
, 
, and 
.
The correct answer is A.
To eliminate K and x in the first equation (the only equation in which y appears), use the second and third equations to replace K and x with expressions involving only N and T. Then solve for y in terms of N and T.
Alternatively, the algebraic manipulations involved in solving this type of problem as above can often be replaced with numerical computations by assigning values to the variables. The assigned values need to be consistent with all the constraints in the problem, and, for efficiency, the assigned values should be chosen to minimize the numerical computations. Letting K = 10, it follows from T =
and x = 5 – T that T = 2 and x = 3. Using these numerical values, the question can be rephrased as follows.If N =
, then which of the following expresses y in terms of N ?
Letting y = 1, it follows that N =
= 2. Plugging N = 2 into A, B, C, D, and E above gives, respectively, 1, –1, , , and .The correct answer is A.
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