To solve the given system of equations by substitution, we follow these steps:

Step 1: Write the system of equations

1. $7x - 3y = -25$
2. $4x + 5 = y$

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Step 2: Substitute $y = 4x + 5$ into the first equation

Since $y$ is expressed in terms of $x$, substitute $4x + 5$ for $y$ in the first equation:

$7x - 3(4x + 5) = -25$

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Step 3: Simplify the equation

Distribute $-3$ over $4x + 5$:

$7x - 12x - 15 = -25$

Combine like terms:

$-5x - 15 = -25$

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Step 4: Solve for $x$

Add $15$ to both sides:

$-5x = -10$

Divide both sides by $-5$:

$x = 2$

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Step 5: Solve for $y$

Substitute $x = 2$ into $y = 4x + 5$:

$y = 4(2) + 5$

$y = 8 + 5 = 13$

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Final Answer:

The solution to the system is:

$\boxed{(x, y) = (2, 13)}$

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Would you like a detailed explanation for any step? Let me know! 😊

Here are 5 related questions to explore further:

1. What are the advantages of solving systems of equations using substitution versus elimination?
2. How can you graphically verify the solution $(2, 13)$?
3. What happens if the system of equations has no solution or infinitely many solutions?
4. Can substitution work for systems with three variables?
5. How does substitution compare to matrix methods for solving systems of equations?

Tip: Always substitute your solution back into both equations to verify correctness.