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The image contains a system of linear equations that needs to be solved. The equations provided are:

\[
\begin{aligned}
1.\quad & x + y = 3z \\
2.\quad & 3x + 5y - 4z = 17 \\
3.\quad & 4y + 2z = 7
\end{aligned}
\]

### Let's solve this system using substitution or elimination methods.

1. **From the first equation:**  
   \[
   x + y = 3z \implies x = 3z - y \quad \text{(Equation 4)}
   \]

2. **Substitute \(x = 3z - y\) into the second equation:**
   \[
   3(3z - y) + 5y - 4z = 17
   \]
   Simplify and solve for \(z\):
   \[
   9z - 3y + 5y - 4z = 17 \implies 5z + 2y = 17 \quad \text{(Equation 5)}
   \]

3. **Now we have two equations:**
   \[
   5z + 2y = 17 \quad \text{(Equation 5)}
   \]
   \[
   4y + 2z = 7 \quad \text{(Equation 3)}
   \]

4. **Eliminate \(z\) by manipulating these equations:**

   Multiply Equation 3 by 2:
   \[
   8y + 4z = 14 \quad \text{(Equation 6)}
   \]
   Subtract Equation 5 from Equation 6:
   \[
   (8y + 4z) - (5z + 2y) = 14 - 17
   \]
   Simplify:
   \[
   6y - z = -3 \quad \text{(Equation 7)}
   \]

5. **Solve Equation 7 for \(z\):**
   \[
   z = 6y + 3 \quad \text{(Equation 8)}
   \]

6. **Substitute Equation 8 into Equation 5:**
   \[
   5(6y + 3) + 2y = 17
   \]
   Simplify and solve for \(y\):
   \[
   30y + 15 + 2y = 17 \implies 32y = 2 \implies y = \frac{1}{16}
   \]

7. **Now substitute \(y = \frac{1}{16}\) back into Equation 8:**
   \[
   z = 6\left(\frac{1}{16}\right) + 3 = \frac{3}{8} + 3 = \frac{27}{8}
   \]

8. **Substitute \(y = \frac{1}{16}\) and \(z = \frac{27}{8}\) into Equation 4:**
   \[
   x = 3\left(\frac{27}{8}\right) - \frac{1}{16} = \frac{81}{8} - \frac{1}{16} = \frac{161}{16}
   \]

Thus, the solution to the system is:

\[
x = \frac{161}{16}, \quad y = \frac{1}{16}, \quad z = \frac{27}{8}
\]

Would you like more details, or do you have any questions about this solution?

### Related Questions:

1. How can the Gaussian elimination method be applied to solve this system?
2. What are the advantages of using substitution over elimination in solving systems of linear equations?
3. Can this system of equations be solved graphically?
4. How would the solution change if the coefficients of the equations were different?
5. How can matrix algebra be used to solve this system?

**Tip:** When solving systems of equations, always check if one method is simpler or more direct than others for a specific problem!

The query submitted by the user and the corresponding solution:

Learn how to solve a system of linear equations using the substitution and elimination methods with a detailed step-by-step solution. This problem covers key concepts in algebra, including linear equations and methods for solving them. Suitable for students in Grades 10-12.

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