Question 467372: If x + y is 4 more than x - y which of the following statements must be true?
I. x = 2
II. y = 2
III. xy has more than one value
A) I only
B) II only
C) III only
D) I and III only
E) II and III only
Thank you!
Found 2 solutions by jim_thompson5910, Theo:
Answer by jim_thompson5910(35256)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the way I see it, selections I, II, and III are all true.
that does not appears to be one of the possible answers though.
the answer to the problem is that y = 2 and x can be any value.
selection I says that x = 2.
this is true, but it doesn't state that x can also be any other value, so this statement has to be false, or at least misleading.
selection II says that y = 2.
this is true.
y has to be equal to 2.
no other value of 2 will satisfy the equation.
selection III says that x * y has more than one value.
this is also true.
y has to be equal to 2 but x can be any value so the product of x and y can have multiple values depending on the value of x.
i would say your answer has to be E) II and III only.
even though I is also true, it is not completely true so, if i had to pick one of the answers to discard, it would have to be I.
by the way:
the equation resulting from your problem statement is:
x + y = x - y + 4
add y to both sides of this equation and you get:
x + 2y = x + 4
subtract x from both sides of this equation and you get:
2y = 4
divide both sides of this equation by 2 and you get:
y = 2
that's the solution for y.
substituting for y in the original equation gets you:
x + y = x - y + 4 becomes:
x + 2 = x - 2 + 4 which becomes:
x + 2 = x + 2
subtract 2 from both sides of this equation and you get:
x = x
that's an identity equation which means that x can be any value.
subtract x from both sides of the equation and you get:
0 = 0
x disappears and the equation is true.
that's another indication that x can be any value and the original equation will be true.
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