We are given two pieces of information about two numbers:

1. The sum of the two numbers is 22:
   $x + y = 22$

2. The difference between the first number and the second number is 8:
   $x - y = 8$

Now, we can solve this system of equations to find the values of $x$ and $y$.

Step 1: Add the two equations

To eliminate $y$, we can add the two equations: $(x + y) + (x - y) = 22 + 8$ Simplifying: $2x = 30$ Now, solve for $x$: $x = \frac{30}{2} = 15$

Step 2: Substitute $x = 15$ into one of the original equations

We can substitute $x = 15$ into the first equation $x + y = 22$: $15 + y = 22$ Solve for $y$: $y = 22 - 15 = 7$

Final Answer:

The two numbers are: $x = 15 \quad \text{and} \quad y = 7$

Would you like more details or have any questions?

Related Questions:

1. How can we solve a system of equations using substitution?
2. What is the geometric interpretation of the solution to a system of equations?
3. How would the solution change if the sum was 20 instead of 22?
4. How can we check if our solution is correct?
5. How would this change if there were more than two equations?

Tip: When solving systems of equations, adding or subtracting equations is often a great way to eliminate one of the variables.