To solve the given problem, the corresponding angles in the diagram suggest relationships due to parallel lines and transversal rules. Let us analyze the given equations and their relationships:

From the diagram:

1. $2x + 4$ and $3x - 1$ are corresponding angles. Therefore: $2x + 4 = 3x - 1$

2. $3y$ and $2y + 2$ are also corresponding angles. Therefore: $3y = 2y + 2$

Solving these equations:

Step 1: Solve $2x + 4 = 3x - 1$

$2x + 4 = 3x - 1$ Subtract $2x$ from both sides: $4 = x - 1$ Add 1 to both sides: $x = 5$

Step 2: Solve $3y = 2y + 2$

$3y = 2y + 2$ Subtract $2y$ from both sides: $y = 2$

Final Solution:

$x = 5, \; y = 2$

If you have any questions or need further explanations, let me know.

Related Questions:

1. How are corresponding angles used in geometric problems involving parallel lines?
2. What are other types of angle relationships formed by transversals (e.g., alternate interior angles)?
3. How can you check your solutions for such equations involving geometry?
4. What are the properties of parallel lines and transversals in real-world applications?
5. How can this method be extended to 3D geometry with planes and lines?

Tip: Always check the relationships between angles (corresponding, alternate, or supplementary) to set up the correct equations.