Let’s denote the two numbers as x and y.
We are given two equations based on the information provided:
- The sum of the numbers: x + y = 19
- The difference of the numbers: x – y = 7
We can solve these equations step by step.
First, let’s rearrange the second equation to express x in terms of y:
x = y + 7
Now we can substitute this expression for x into the first equation:
(y + 7) + y = 19
Combining like terms gives:
2y + 7 = 19
Now, subtract 7 from both sides:
2y = 12
Dividing both sides by 2 gives:
y = 6
Now that we have the value of y, we can find x using the expression we derived earlier:
x = y + 7 = 6 + 7 = 13
Therefore, the two numbers are 13 and 6.
In conclusion, the numbers you are looking for are 13 and 6.