Suppose that two parallelograms are similar. then suppose that one of them is rotated, and after the rotation the parallelograms are still similar. which of the following statements must be true?
a. the parallelogram must have been rotated by 90°.
b. the parallelogram must have been rotated by 180°.
c. the parallelogram must have been rotated by 360°.
d. the parallelogram could have been rotated by any number of degrees.

D.The parallelogram could have been rotated by any number of degrees.

If the two parallelograms are only parallelograms, then B would be the correct answer. However, a Square is by definition a parallelogram, and the statement only says that the objects are parallelograms, not that they are not squares. If they were squares, then A could be correct, but D would still be incorrect. However, since we're asked which statement must be correct, and it isn't necessary that they are squares, we have to conclude that B is the only correct answer.

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.