The problem in the image states:

"The sum of two numbers is 45 and their difference is 9. Create and solve a system to determine the two numbers. Answer in a complete sentence."

Step 1: Define variables

Let:

• $x$ be the first number.
• $y$ be the second number.

Step 2: Set up the system of equations

1. The sum of the two numbers is 45: $x + y = 45$
2. The difference of the two numbers is 9: $x - y = 9$

Step 3: Solve the system

We can solve this system using either substitution or elimination. Here, we'll use elimination:

1. Add the two equations: $(x + y) + (x - y) = 45 + 9$ Simplifying: $2x = 54$ Solving for $x$: $x = 27$

2. Substitute $x = 27$ into the first equation $x + y = 45$: $27 + y = 45$ Solving for $y$: $y = 18$

Final Answer:

The two numbers are 27 and 18.

Complete sentence:

The two numbers are 27 and 18.

Would you like any further details or have any questions about this solution?

Here are 5 related questions:

1. What happens if the sum of the two numbers is changed to 50 but the difference remains 9?
2. Can you solve the system using substitution instead of elimination?
3. What if the difference between the two numbers is negative, e.g., -9?
4. How would the solution change if the two numbers were fractions or decimals?
5. Can this problem be solved graphically? How would the lines representing these equations intersect?

Tip: When solving a system of linear equations, elimination works well when both equations are already aligned, while substitution is useful if one equation is easy to solve for a single variable.