https://file.aiquickdraw.com/mathbot/file/1736435278561h5i29vrz.jpg

The system of equations given in the image is:

\[
\begin{cases} 
x - y = 5 \\
3x - 5y = 5
\end{cases}
\]

Let's solve it step by step:

---

### 1. Solve the first equation for \(x\) in terms of \(y\):
From \(x - y = 5\), we get:
\[
x = y + 5
\]

---

### 2. Substitute \(x = y + 5\) into the second equation:
Substitute \(x\) into \(3x - 5y = 5\):
\[
3(y + 5) - 5y = 5
\]

Simplify:
\[
3y + 15 - 5y = 5
\]

Combine like terms:
\[
-2y + 15 = 5
\]

Subtract 15 from both sides:
\[
-2y = -10
\]

Divide by \(-2\):
\[
y = 5
\]

---

### 3. Substitute \(y = 5\) back into \(x = y + 5\):
\[
x = 5 + 5 = 10
\]

---

### 4. Solution:
The solution to the system of equations is:
\[
(x, y) = (10, 5)
\]

The solution set is:
\[
\{(10, 5)\}
\]

---

Would you like me to verify the solution or provide additional steps? 

Here are 5 related questions to expand your understanding:
1. What is the graphical interpretation of solving a system of equations like this one?
2. How can we determine if a system of equations has no solution or infinitely many solutions?
3. How can substitution be replaced by the elimination method?
4. What happens if the two equations represent parallel lines?
5. How do we solve a system of three equations with three variables?

**Tip**: Always double-check your solution by substituting the values back into the original equations!

Find the solution set for the system of equations: x - y = 5 and 3x - 5y = 5.

Learn how to solve the system of linear equations x - y = 5 and 3x - 5y = 5 using the substitution method. This detailed explanation covers key algebraic concepts, making it suitable for students in Grades 8-10.

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