For each of the following equations, determine which of the following statements are true:
(1) For all real numbers x, there exists a real number y such that the equation is true.
(2) There exists a real number x, such that for all real numbers y, the equation is true.
Note that it is possible for both statements to be true or for both to be false.
a. 2x + y = 7
b. y + x = x + y
c. x2 − 2xy + y2 = 0
d. (x − 5)(y − 1) = 0
e. x2 + y2 = − 1
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