the sum of two integers is zero. the difference of the same two integers is 16. What are the integers
8 + (-8) = 0
8 - (-8) = 16
To find the two integers, let's assign variables:
Let's assume the first integer is x and the second integer is y.
We are given two pieces of information:
1. The sum of the two integers is zero, which can be written as: x + y = 0.
2. The difference of the same two integers is 16, which can be written as: x - y = 16.
Now we have a system of two equations:
Equation 1: x + y = 0
Equation 2: x - y = 16
We can solve this system by using the method of elimination or substitution. Let's use the method of elimination:
To eliminate the y variable, we can add Equation 1 to Equation 2:
(x + y) + (x - y) = 0 + 16
Simplifying the equation:
2x = 16
Dividing both sides by 2:
x = 8
Now, substitute the value of x into one of the original equations, let's use Equation 1:
8 + y = 0
Subtracting 8 from both sides:
y = -8
Therefore, the two integers that satisfy the given conditions are 8 and -8.