https://file.aiquickdraw.com/mathbot/file/1726610812349je1z4nb0.jpg

The system of equations shown in the image is:

\[
x = -y + 5
\]
\[
-3x + 7y = 45
\]

### Step-by-Step Solution (Using Substitution):

1. **Substitute** \( x = -y + 5 \) into the second equation \( -3x + 7y = 45 \):

\[
-3(-y + 5) + 7y = 45
\]

2. **Simplify** the equation:

\[
3y - 15 + 7y = 45
\]

\[
10y - 15 = 45
\]

3. **Solve for** \( y \):

\[
10y = 45 + 15
\]

\[
10y = 60
\]

\[
y = 6
\]

4. **Substitute** \( y = 6 \) back into the equation \( x = -y + 5 \):

\[
x = -6 + 5
\]

\[
x = -1
\]

### Final Solution:
\[
x = -1, \quad y = 6
\]

Let me know if you'd like more details or have any questions!

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Here are 5 related questions for further exploration:

1. How do you solve a system of equations using the elimination method?
2. What are the key differences between substitution and elimination methods in solving systems of equations?
3. Can you solve a system of equations graphically? How does it differ from algebraic methods?
4. What are some real-life applications of systems of equations?
5. How do you know if a system of equations has no solution, one solution, or infinitely many solutions?

**Tip:** Always double-check your substituted values by plugging them back into the original equations to verify correctness!

Solve the system of equations: x = -y + 5 and -3x + 7y = 45 by substitution.

Learn how to solve the system of equations x = -y + 5 and -3x + 7y = 45 using the substitution method. This step-by-step guide simplifies the process and is perfect for students in Grades 8-10 learning algebraic methods for solving equations.

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