The sum of two numbers is 14. The difference of the numbers is 2. What are the numbers

See my answer below.

6 and8

To find the two numbers that satisfy the given conditions, we can set up a system of equations and solve them simultaneously.

Let's assume the two numbers are x and y.

From the given information, we can form two equations:

Equation 1: x + y = 14 (The sum of the two numbers is 14)
Equation 2: x - y = 2 (The difference of the two numbers is 2)

Now, we can solve this system of equations to find the values of x and y.

There are different methods to solve a system of equations, such as substitution, elimination, or using matrices. In this case, let's use the method of elimination:

Adding both equations, we get:

(x + y) + (x - y) = 14 + 2
2x = 16
Dividing both sides by 2, we find:
x = 8

Substituting the value of x into Equation 1, we can solve for y:

8 + y = 14
y = 14 - 8
y = 6

Therefore, the two numbers are 8 and 6.