Final answer:
The two numbers are 33 and 25, found by setting up a system of two equations from the given sum and difference and solving them simultaneously.
Step-by-step explanation:
The sum of two numbers is 58 and the difference is 8. To find these two numbers, we can set up a system of two equations to solve them simultaneously. Let's denote the first number as x and the second number as y.
The equations based on the information given would be:
x + y = 58 (Equation 1: Sum)
x - y = 8 (Equation 2: Difference)
We can solve these equations using either substitution or elimination. For simplicity, let's use the elimination method. If we add the two equations, the 'y' terms will cancel out:
(x + y) + (x - y) = 58 + 8
2x = 66
x = 33
Now that we have the value of x, we can substitute it back into either of the original equations to find y:
33 + y = 58
y = 25
Therefore, the two numbers are 33 and 25.