1. **State the problem:** Solve the system of equations using the elimination method: $$3x - 2y = 38$$ $$x = 6 - y$$ 2. **Rewrite the second equation:** Express $x$ in terms of $y$: $$x = 6 - y$$ 3. **Substitute $x$ into the first equation:** Replace $x$ in the first equation with $6 - y$: $$3(6 - y) - 2y = 38$$ 4. **Simplify the equation:** $$18 - 3y - 2y = 38$$ $$18 - 5y = 38$$ 5. **Isolate $y$:** Subtract 18 from both sides: $$18 - 5y - 18 = 38 - 18$$ $$\cancel{18} - 5y - \cancel{18} = 20$$ $$-5y = 20$$ 6. **Solve for $y$:** Divide both sides by $-5$: $$\frac{-5y}{\cancel{-5}} = \frac{20}{\cancel{-5}}$$ $$y = -4$$ 7. **Find $x$:** Substitute $y = -4$ back into $x = 6 - y$: $$x = 6 - (-4)$$ $$x = 6 + 4 = 10$$ **Final answer:** $$x = 10, \quad y = -4$$