1. **State the problem:** We are given a quadrilateral ABCD with sides labeled as follows: CB = $2y - 4$, CD = $4x$, BA = $x + 9$, and DA = $y$. We need to find the values of $x$ and $y$. 2. **Analyze the figure and given information:** The quadrilateral has diagonals intersecting, which suggests it might be a parallelogram or another special quadrilateral where opposite sides are equal. 3. **Use properties of quadrilaterals:** If ABCD is a parallelogram, opposite sides are equal: $$CB = DA \quad \text{and} \quad CD = BA$$ 4. **Set up equations:** From $CB = DA$: $$2y - 4 = y$$ From $CD = BA$: $$4x = x + 9$$ 5. **Solve the first equation:** $$2y - 4 = y$$ Subtract $y$ from both sides: $$2y - y - 4 = 0 \implies y - 4 = 0$$ Add 4 to both sides: $$y = 4$$ 6. **Solve the second equation:** $$4x = x + 9$$ Subtract $x$ from both sides: $$4x - x = 9 \implies 3x = 9$$ Divide both sides by 3: $$x = 3$$ 7. **Final answer:** $$x = 3, \quad y = 4$$