1. **State the problem:** Solve the system of linear equations: $$2x + y = 7$$ $$x - 2y = 6$$ 2. **Formula and method:** We will use the substitution or elimination method to find values of $x$ and $y$ that satisfy both equations. 3. **Step 1: Express $y$ from the first equation:** $$y = 7 - 2x$$ 4. **Step 2: Substitute $y$ into the second equation:** $$x - 2(7 - 2x) = 6$$ 5. **Step 3: Simplify and solve for $x$:** $$x - 14 + 4x = 6$$ $$5x - 14 = 6$$ $$5x = 20$$ $$x = 4$$ 6. **Step 4: Substitute $x = 4$ back into $y = 7 - 2x$ to find $y$:** $$y = 7 - 2(4) = 7 - 8 = -1$$ 7. **Final answer:** $$x = 4, \quad y = -1$$ This means the solution to the system is the point $(4, -1)$ where both lines intersect.