1. **Problem statement:** Solve the linear system using the Gleichsetzungsverfahren (substitution by setting equal). Given system 2a: $$x + y = 10$$ $$x - y = 0$$ 2. **Formula and method:** The Gleichsetzungsverfahren involves expressing one variable from each equation and setting them equal to find the solution. 3. **Step 1:** From the second equation, solve for $x$: $$x - y = 0 \implies x = y$$ 4. **Step 2:** Substitute $x = y$ into the first equation: $$y + y = 10$$ $$2y = 10$$ 5. **Step 3:** Simplify and solve for $y$: $$\cancel{2}y = \cancel{2}5$$ $$y = 5$$ 6. **Step 4:** Substitute $y = 5$ back into $x = y$: $$x = 5$$ 7. **Final answer:** $$\boxed{x = 5, y = 5}$$ This means the solution to the system is the point $(5,5)$ where both equations intersect.