1. **State the problem:** Solve the system of linear equations: $$4x + 2y = 7$$ $$-x - y = 6$$ 2. **Formula and rules:** We can solve this system using substitution or elimination. Here, elimination is convenient. 3. **Step 1: Multiply the second equation by 2 to align coefficients of $y$:** $$-2x - 2y = 12$$ 4. **Step 2: Add the first equation and the modified second equation:** $$4x + 2y + (-2x - 2y) = 7 + 12$$ $$ (4x - 2x) + (2y - 2y) = 19$$ $$2x + 0 = 19$$ $$2x = 19$$ 5. **Step 3: Solve for $x$:** $$x = \frac{19}{2} = 9.5$$ 6. **Step 4: Substitute $x = 9.5$ into the second original equation:** $$-x - y = 6$$ $$-9.5 - y = 6$$ 7. **Step 5: Solve for $y$:** $$-y = 6 + 9.5 = 15.5$$ $$y = -15.5$$ **Final answer:** $$x = 9.5, \quad y = -15.5$$