We have two equations to solve simultaneously:

1. \( 7x - 4y = 5 \)
2. \( 7x - y = -4 \)

We will solve this system using the **elimination method**.

### Step 1: Eliminate one variable
Subtract the second equation from the first to eliminate \(x\):

\[
(7x - 4y) - (7x - y) = 5 - (-4)
\]

Simplifying the equation:

\[
7x - 4y - 7x + y = 5 + 4
\]

\[
-3y = 9
\]

### Step 2: Solve for \(y\)

\[
y = \frac{9}{-3} = -3
\]

### Step 3: Substitute \(y = -3\) into one of the original equations
We'll substitute it into the second equation:

\[
7x - (-3) = -4
\]

\[
7x + 3 = -4
\]

### Step 4: Solve for \(x\)

\[
7x = -4 - 3
\]

\[
7x = -7
\]

\[
x = \frac{-7}{7} = -1
\]

### Final Solution
The solution to the system of equations is:

\[
x = -1, \quad y = -3
\]

Would you like more details or have any questions?

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Here are some related questions:

1. What is the substitution method for solving systems of equations?
2. How do you check the solution to a system of equations?
3. Can systems of equations have no solution or infinite solutions?
4. What are other methods to solve systems of linear equations?
5. How do systems of equations relate to real-world problems?

**Tip:** When using the elimination method, always simplify carefully to avoid sign errors!

Learn how to solve the system of linear equations 7x - 4y = 5 and 7x - y = -4 using the elimination method. This detailed guide walks through step-by-step algebraic solutions, eliminating variables and solving for x and y. Suitable for Grades 8-10 students studying algebra and systems of equations.

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