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We are tasked with solving a system of equations using the substitution method. The given system is:

\[
\begin{aligned}
1. & \quad x - y = 1 \\
2. & \quad 4x + 3y = 25
\end{aligned}
\]

### Step-by-Step Solution:

1. **Solve the first equation for \(x\):**

\[
x - y = 1 \quad \Rightarrow \quad x = y + 1
\]

2. **Substitute this expression for \(x\) into the second equation:**

\[
4(y + 1) + 3y = 25
\]

3. **Expand and simplify:**

\[
4y + 4 + 3y = 25 \quad \Rightarrow \quad 7y + 4 = 25
\]

4. **Solve for \(y\):**

\[
7y = 25 - 4 \quad \Rightarrow \quad 7y = 21 \quad \Rightarrow \quad y = \frac{21}{7} = 3
\]

5. **Substitute \(y = 3\) back into the expression for \(x\):**

\[
x = y + 1 = 3 + 1 = 4
\]

### Final Solution:

\[
(x, y) = (4, 3)
\]

Do you need further details or have any questions?

### Related Questions:
1. Can this system of equations be solved using the elimination method?
2. How can we verify the solution of a system of equations?
3. What are the differences between the substitution and elimination methods?
4. Can this system be solved graphically, and how would the graph look?
5. What is the general approach to solving nonlinear systems using substitution?

### Tip:
Always verify your solutions by substituting the values back into the original system to ensure they satisfy both equations.

Use the substitution method to find all solutions of the system of equations:

x - y = 1
4x + 3y = 25

Learn how to solve a system of linear equations using the substitution method with a step-by-step solution. This example covers the equations x - y = 1 and 4x + 3y = 25. Suitable for Grades 8-10 students.

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