To find the two numbers given that their sum is 14 and their difference is 6, we can set up a system of equations. Let the two numbers be represented by x and y.
We can formulate the first equation based on the sum:
- x + y = 14
And the second equation based on the difference:
- x – y = 6
Now, we can solve this system step-by-step:
- From the first equation, express x in terms of y:
- x = 14 – y
- Substitute x into the second equation:
- (14 – y) – y = 6
- Simplifying, we get:
- 14 – 2y = 6
- 2y = 14 – 6
- 2y = 8
- y = 4
- Now substitute y back into the expression for x:
- x = 14 – 4
- x = 10
Thus, the two numbers are x = 10 and y = 4.
We can double-check our work:
- Sum: 10 + 4 = 14
- Difference: 10 – 4 = 6
Both conditions are satisfied, confirming that the two numbers are indeed 10 and 4.