To find the two numbers, let’s define them as x and y. We know two things from the problem:
- The sum of the two numbers: x + y = 19
- The difference of the two numbers: x – y = 7
Now, we can solve these equations step by step.
First, we can use the first equation to express x in terms of y:
- x = 19 – y
Next, we can substitute this expression for x into the second equation:
- (19 – y) – y = 7
Now simplify this equation:
- 19 – 2y = 7
Next, solve for y:
- -2y = 7 – 19
- -2y = -12
- y = 6
Now that we have y, we can find x using the first equation:
- x = 19 – 6
- x = 13
Thus, the two numbers are 13 and 6. To verify, we can check the original conditions:
- Sum: 13 + 6 = 19
- Difference: 13 – 6 = 7
Both conditions are satisfied, confirming that the numbers we found are correct.