This is a parallelogram, and we need to solve for the variables $x$ and $y$.

In a parallelogram:

1. Opposite sides are equal.
   • So, $5x - 6 = 3x$.
   • $\frac{1}{2}y = 4$.

Step-by-step solution:

1. Solve for $x$:
   From $5x - 6 = 3x$: $5x - 3x = 6$ $2x = 6 \quad \Rightarrow \quad x = 3.$

2. Solve for $y$:
   From $\frac{1}{2}y = 4$: $y = 4 \times 2 \quad \Rightarrow \quad y = 8.$

Final Values:

• $x = 3$
• $y = 8$

Would you like further explanation or have additional questions?

Related Questions:

1. What are the properties of a parallelogram and how can they be used in different scenarios?
2. How do we solve equations with multiple variables in geometry problems?
3. What is the significance of opposite sides being equal in a parallelogram?
4. Can we verify these results by substituting back into the equations?
5. How do these relationships extend to special parallelograms, like rhombuses or rectangles?

Tip:

Always start by identifying geometric properties that can simplify your equations, such as equal sides or supplementary angles in parallelograms!