Huzefa K. answered 04/13/14
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Math Teacher|Michigan + Northwestern Law|Perfect Score Math ACT + SAT
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:"
x2 + y2 = 2
By 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 + y2 = 2
2y2 = 2
y2 = 1
y = 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