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Let's break down the problem and formulate a system of equations step by step.

We are asked to use the variables \(x\), \(y\), and \(z\) for quantities \(X\), \(Y\), and \(Z\), respectively.

### Given Information:
1. **The sum of the three quantities is 151.**
   \[
   x + y + z = 151
   \]
2. **Four of quantity \(X\) (which is \(x\)) and three of quantity \(Y\) (which is \(y\)) is 2 more than quantity \(Z\) (which is \(z\)).**
   \[
   4x + 3y = z + 2
   \]
3. **Quantity \(Y\) subtracted from quantity \(X\) is 9.**
   \[
   x - y = 9
   \]

### System of Equations:
1. \( x + y + z = 151 \)
2. \( 4x + 3y = z + 2 \)
3. \( x - y = 9 \)

This is the system of equations you need to solve. Would you like me to solve the system for you or explain any specific step in more detail? 

Here are 5 related questions for practice:
1. How would you solve this system of equations using substitution?
2. Can this system be solved using the elimination method?
3. What is the significance of each equation in the system?
4. How do you interpret the second equation in terms of balancing the quantities?
5. What happens to the system if you change the sum in the first equation?

**Tip:** When dealing with word problems, translating verbal descriptions into mathematical equations is key to forming a solvable system.

Formulate a system of equations from the description below. Use the variables x, y and z for Quantity X, Y, and Z, respectively. The sum of three quantities is 151. Four of quantity X and three of quantity Y is 2 more than Quantity Z. Quantity Y subtracted from Quantity X is 9.

Learn how to solve a system of equations involving three variables (X, Y, and Z) with algebraic methods. The problem asks for the sum of quantities, relationship between quantities, and differences. Suitable for high school algebra students.

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