The sum of two numbers is 14 and their difference is 6 what are the two numbers?

To find the two numbers, we can set up a system of equations based on the information given.

Let’s denote the two numbers as x and y.

• The first piece of information tells us that the sum of the two numbers is 14, so we can write the equation:
• x + y = 14
• The second piece of information tells us that the difference between the two numbers is 6, giving us another equation:
• x – y = 6

Now we have the following system of equations:

1. x + y = 14
2. x – y = 6

To solve this, we can add both equations together:

(x + y) + (x – y) = 14 + 6

This simplifies to:

2x = 20

Now, we can solve for x:

x = 20 / 2 = 10

Now that we have x, we can substitute it back into one of the original equations to find y. Using the first equation:

10 + y = 14

This simplifies to:

y = 14 – 10 = 4

Therefore, the two numbers are 10 and 4.

To verify:

• Sum: 10 + 4 = 14
• Difference: 10 – 4 = 6

Both conditions are satisfied, confirming our solution.