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  3. If, which of the following could be the value of y ?

If, which of the following could be the value of y ?

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问题 If, which of the following could be the value of y ?
选项 A、4
B、1
C、-1
D、-3
E、-5
答案D
解析 One approach to answer the question is to solve the equation for y as follows.
2(2y-3)=y(3-y)
4y - 6 = 3y - y2
y2 +y -6 = 0
(y + 3)(y-2)= 0
Since a product equals 0 only if at least one of the factors equals 0,
y + 3 = 0 or y - 2 = 0
y = -3 or y = 2
Thus, there are two values of y that satisfy the equation, —3 and 2. The value -3 is Choice D, and the value 2 is not among the answer choices. The correct answer is Choice D.
    Another approach is to determine, for each answer choice, whether the equation holds. To do this, you can substitute the answer choice for y in the equation, replace the equals sign in the equation by the place-holder symbol, and then simplify to see whether the two expressions are in fact equal.
    For Choice A, substituting y = 4 in the equationand replacing the equals sign = with the placeholder symbolyields the relationship , which can be simplified as follows.

Since, you can conclude that the placeholder symbol does not represent equality, and therefore the equation does not hold for y = 4.
    If you continue evaluating the answer choices, you will find that the correct answer is Choice D, -3. To see that the equationis true when y = -3, substitute y = -3 in the equation and replace the equals sign = with the placeholder symbol. This yields the relationship. This relationship can be simplified as follows.

Since 3 = 3, you can conclude that the placeholder symbol represents equality, and therefore the equation holds for y = -3. The correct answer is Choice D.
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