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!

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!