2012-02-29 09:00:08

If |x - 2| + 6 = 9, and |y + 3| + 4 = 11, then xy could be:

A) -10
B) -5
C) -4
D) 4
E) 50

The correct answer is C

Explanation: Take the equations one at a time and start by isolating the absolute values. Starting with the x equation:

|x - 2| + 6 = 9 turns into |x - 2| = 3 after we subtract 6 from both sides.

Now, remove the absolute value sign by writing two separate equations, one for a positive outcome and one for a negative one.

x - 2 = -3      x - 2 = 3

Solve for x, and you'll find that x could equal -1 or 5.

Now, turn to the y equation.

|y + 3| + 4 = 11 turns into |y + 3| = 7 after we subtract 4 from both sides.

Now, remove the absolute value sign by making the outcome positive and negative.

y + 3 = 7       y + 3 = -7

Solve for y in both equations, and you'll find that y could equal 4 or -10.

The last step in finding the answer is to multiply both y values by both x values to find the four potential answers. Then, see which result matches one of the answer choices. Multiplying each y by each x value gives you the following results: -4, 10, -50, and 20. Of those, only -4 is an answer choice, so that COULD be the answer, making C the answer to the question. Keep in mind, of course, that all of your four results could be the answer, but only -4 actually is an answer choice.