Huzefa K. answered • 04/13/14

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You can start this problem by writing out the words in equations. So, your two numbers are x and y. Let's begin with "the sum of two numbers is 0:"

x + y = 0

Next, let's write the second statement as an equation, "the sum of their squares is 2:"

x

^{2}+ y^{2}= 2By using substitution based on the first equation, you can simplify the second equation. We know x + y = 0; we then know that x = -y. Now, using substitution, the second equation becomes:

(-y)

^{2}+ y^{2}= 22y

^{2}=^{ }2y

^{2}= 1y = 1, -1

Now, to get x, simply plug y into the first equation:

x + y = 0

When y = 1, then:

x + 1 = 0

x = -1

And when y = -1:

x - 1 = 0

x = 1

So the solution sets are:

(1, -1) or (-1, 1)

Since the order doesn't matter, and I arbitrarily assigned x and y, the final answer is simply:

**1, -1**