2012-05-11 09:00:43

What is a possible value of xy if x² + 7x + 10 = 0 and y² + 2x +1 = 0?



The correct answer is 2 or  5

Explanation: Start by factoring out the two equations.

x² + 7x + 10 = 0 can be factored to (x + 5)(x + 2) = 0 (the trick here is to look for two numbers that add together to be 7 and multiply to be 10). This means that either x + 5 = 0 or x + 2 = 0. This means that x = -2 or - 5 (from subtracting 5 and 2 from both sides of their respective equations).

Do the same thing for the y equation: y² + 2x +1 = 0 simplifies to (y + 1)(y + 1) = 0, meaning y + 1 = 0, making y = -1.

Multiply either x term by y to get -5 x -1 = 5, or -2 x -1 = 2. This means either 2 or 5 would be acceptable answers to grid in on your answer sheet.