1. **State the problem:** We are given the vector equation $(x - y, 2x - y) = (1, 6)$ and need to find the values of $x$ and $y$. 2. **Set up the system of equations:** Since the vectors are equal, their corresponding components must be equal: $$x - y = 1$$ $$2x - y = 6$$ 3. **Solve the system:** - From the first equation, express $y$ in terms of $x$: $$y = x - 1$$ - Substitute $y = x - 1$ into the second equation: $$2x - (x - 1) = 6$$ $$2x - x + 1 = 6$$ $$x + 1 = 6$$ $$x = 5$$ - Substitute $x = 5$ back into $y = x - 1$: $$y = 5 - 1 = 4$$ 4. **Final answer:** $$x = 5, \quad y = 4$$