SOLUTION: 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 an

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): You can put this solution on YOUR website!
"If x + y is 4 more than x - y", then . Now solve for y:

So the answer is choice II.

Note: x can be ANY number, so it's not choice I. Choice III doesn't make sense, so that can be thrown out too.

So this means that the answer is choice B) II only
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.

RELATED QUESTIONS
If x is an integer greater than 1 and if y = x + (1/x), which of the following (answered by jim_thompson5910)
If (x^2)(y^3)z < 0, which of the following statements must be true? I. yz < 0 II. xz... (answered by richard1234)
If xy>0 and xz<0, which of the following statements must be true? I. x+y+z>0 II.... (answered by ikleyn)
If xy > 1 and z < 0, which of the following statements must be true? I. x > z II. (answered by jim_thompson5910)
If x(x - y) = 0 and x > y, which of the following statements must be true? I. x =... (answered by jim_thompson5910)
A certain function f has the property that f(x + y) = f(x) + f(y) for all values of x... (answered by robertb)
If x = y and m > y, then which of the following must be true? I. x < m II. x = m (answered by Fombitz)
If X, Y are non-zero integers and X/Y < |X/Y| < Y, which of the following must be true? (answered by greenestamps)
p: The average of x, y, and 8 is 5. q: The sum of x and y is 8. Based on statements p (answered by Jk22)