1. **State the problem:** Solve the system of linear equations: $$3x - 2y = 38$$ $$x = 6 - y$$ 2. **Substitute the expression for $x$ from the second equation into the first:** $$3(6 - y) - 2y = 38$$ 3. **Distribute the 3:** $$18 - 3y - 2y = 38$$ 4. **Combine like terms:** $$18 - 5y = 38$$ 5. **Isolate $y$ by subtracting 18 from both sides:** $$18 - 5y - 18 = 38 - 18$$ $$\cancel{18} - 5y - \cancel{18} = 20$$ $$-5y = 20$$ 6. **Divide both sides by $-5$ to solve for $y$:** $$\frac{-5y}{-5} = \frac{20}{-5}$$ $$y = -4$$ 7. **Substitute $y = -4$ back into the second equation to find $x$:** $$x = 6 - (-4)$$ $$x = 6 + 4 = 10$$ **Final answer:** $$x = 10, \quad y = -4$$