https://file.aiquickdraw.com/mathbot/file/1728860871988gf6gnbrq.jpg

The system of equations from the image is:

\[
\begin{cases}
30 - (8 - x) = 2y + 30 \\
5x - 29 = x - (5 - 4y)
\end{cases}
\]

Let's solve this system step by step:

### First equation: 
\[
30 - (8 - x) = 2y + 30
\]

Simplify the left side:
\[
30 - 8 + x = 2y + 30
\]
\[
22 + x = 2y + 30
\]
Subtract 30 from both sides:
\[
x - 8 = 2y
\]
Solve for \( x \):
\[
x = 2y + 8
\]

### Second equation:
\[
5x - 29 = x - (5 - 4y)
\]

Distribute on the right side:
\[
5x - 29 = x - 5 + 4y
\]
Subtract \( x \) from both sides:
\[
4x - 29 = -5 + 4y
\]
Add 29 to both sides:
\[
4x = 24 + 4y
\]
Now, divide both sides by 4:
\[
x = 6 + y
\]

### Substitution:

We now have two expressions for \( x \):
1. \( x = 2y + 8 \)
2. \( x = 6 + y \)

Set them equal to each other:
\[
2y + 8 = 6 + y
\]
Subtract \( y \) from both sides:
\[
y + 8 = 6
\]
Subtract 8 from both sides:
\[
y = -2
\]

### Solve for \( x \):

Now, substitute \( y = -2 \) into \( x = 6 + y \):
\[
x = 6 + (-2) = 4
\]

### Final solution:
\[
x = 4, \quad y = -2
\]

Would you like further details or clarification on this solution?

### Related Questions:
1. What is the general method for solving systems of linear equations?
2. How can substitution be applied when solving nonlinear systems of equations?
3. What are the possible types of solutions for a system of two linear equations?
4. How can we verify the solution of a system of equations?
5. What are the different methods for solving systems of equations (e.g., substitution, elimination)?

### Tip:
Always check your solution by substituting both values back into the original system of equations to ensure they satisfy both equations!

30 - (8 - x) = 2y + 30, 5x - 29 = x - (5 - 4y)

Learn how to solve a system of linear equations involving two variables using the substitution method. This detailed step-by-step solution covers key algebraic concepts and is suitable for students in Grades 9-11.

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