To write the system of equations for this situation, we need to define variables and translate the problem into mathematical equations:

Variables

Let:

• $x$: The amount of money invested at 10%.
• $y$: The amount of money invested at 12%.
• $z$: The amount of money invested at 15%.

Key Information and Equations

1. Total investment: The total amount invested is $17,000. $x + y + z = 17000$

2. Total income: The total annual income from these investments is $2110. The income is calculated using the interest rates: $0.10x + 0.12y + 0.15z = 2110$

3. Relationship between investments: The amount invested at 12% ($y$) is $1000 less than the sum of the amounts invested at 10% ($x$) and 15% ($z$). $y = x + z - 1000$

Final System of Equations

1. & \quad x + y + z = 17000 \\ 2. & \quad 0.10x + 0.12y + 0.15z = 2110 \\ 3. & \quad y = x + z - 1000 \end{aligned}$$ Would you like me to solve this system or explain it further? --- Here are 5 related questions to expand your understanding: 1. How do we solve systems of linear equations using substitution or elimination? 2. What happens if we graph these equations? How can we interpret the solution geometrically? 3. How would the system change if the annual income or interest rates were different? 4. Can this system of equations have more than one solution? Why or why not? 5. What is the importance of defining variables correctly in word problems? **Tip:** Always organize the problem's information into clear variables and translate step by step into mathematical equations for clarity!