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!