The sum of two numbers is 0 and the sum of their squares is 2.

Question

Word problems solved by two equations

 

Answer 1

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