https://file.aiquickdraw.com/mathbot/file/1726072643759200epbpa.jpg

The system of equations provided is:

\[
\begin{aligned}
1. \ 3x + 5y &= 5 \\
2. \ 7x + 5y &= 25
\end{aligned}
\]

### Solving by Elimination Method:

1. Subtract the first equation from the second to eliminate \(y\):
   \[
   (7x + 5y) - (3x + 5y) = 25 - 5
   \]
   Simplifying:
   \[
   4x = 20
   \]
   Solve for \(x\):
   \[
   x = \frac{20}{4} = 5
   \]

2. Substitute \(x = 5\) into the first equation to solve for \(y\):
   \[
   3(5) + 5y = 5
   \]
   Simplifying:
   \[
   15 + 5y = 5
   \]
   Subtract 15 from both sides:
   \[
   5y = 5 - 15 = -10
   \]
   Solve for \(y\):
   \[
   y = \frac{-10}{5} = -2
   \]

### Solution:
The solution to the system of equations is \(x = 5\) and \(y = -2\).

Would you like more details or have any questions?

Here are 5 related questions you can explore:
1. How do we know that the elimination method is appropriate here?
2. What is the substitution method, and how would it work on this system?
3. How can you graph these equations to find the solution visually?
4. What happens if the system has no solution or infinitely many solutions?
5. What are some common pitfalls when solving systems of equations?

**Tip:** Always check your solution by plugging the values back into both original equations to verify they hold true.

Solve the system of equations: 3x + 5y = 5 and 7x + 5y = 25

Learn how to solve the system of linear equations 3x + 5y = 5 and 7x + 5y = 25 using the elimination method. This problem covers important algebraic concepts and steps for solving systems of equations, suitable for students in Grades 9-11.

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