1. **State the problem:** We are given the system of linear equations: $$x + y + z = 6$$ $$x - y + 3 = 2$$ $$2x + y - z = 1$$ and the proposed solution: $$x=1, y=2, z=3$$. We need to check whether this solution satisfies the system (i.e., test consistency). Then, there is an incomplete second system to find the solution of: $$x + y + z = 2$$ $$x - y + $$ (incomplete). Since the second system is incomplete, we can only comment on the first. 2. **Check the first equation:** Substitute $x=1$, $y=2$, $z=3$ into $$x + y + z = 6$$ Calculation: $$1 + 2 + 3 = 6$$ which simplifies to $$6 = 6$$, true. 3. **Check the second equation:** The second equation is $$x - y + 3 = 2$$ Substituting values: $$1 - 2 + 3 = 2$$ Calculate left side: $$1 - 2 + 3 = 2$$ which simplifies to $$2 = 2$$, true. 4. **Check the third equation:** $$2x + y - z = 1$$ Substitute $x=1$, $y=2$, $z=3$: $$2(1) + 2 - 3 = 1$$ Calculate left side: $$2 + 2 - 3 = 1$$ which simplifies to $$1 = 1$$, true. 5. **Conclusion:** All three equations are satisfied by $x=1$, $y=2$, and $z=3$, so the solution is correct, and the system is consistent. 6. **Second system:** Due to incomplete information for the second system $$x + y + z = 2$$ $$x - y + $$ it's impossible to solve or analyze it further. **Final answer:** The given solution $(x=1,y=2,z=3)$ satisfies the first system, making it consistent.