System A:
Notice that:
![-(-x+5y)=x-5y,](https://img.qammunity.org/2023/formulas/mathematics/college/8k6l7fg3ss99e5uhm8fa0ie9fwx6shbdoq.png)
therefore the first system of equations implies that:
![-5=5,](https://img.qammunity.org/2023/formulas/mathematics/college/txpta9unykcfl8o9ufif0iprn6d1djkb7o.png)
the above result is a contradiction, therefore system A has no solution.
System B:
Notice that:
![-(-x+2y)=x-2y,](https://img.qammunity.org/2023/formulas/mathematics/college/e20emmzukj3rgkk503y1mnkmlnts4fyliv.png)
therefore the second system of equations implies that:
![6=6,](https://img.qammunity.org/2023/formulas/mathematics/college/orgai3agfr0m6vmxe5aaf4cu9n7azik2lc.png)
then the second system has infinitely many solutions, they must satisfy:
![y=(x)/(2)-3.](https://img.qammunity.org/2023/formulas/mathematics/college/twaqkj43236c5g9212gnfgcwce4di8qzcg.png)
Answer:
System A: The system has no solution.
System B: The system has infinitely many solutions, they must satisfy:
![y=(x)/(2)-3.](https://img.qammunity.org/2023/formulas/mathematics/college/twaqkj43236c5g9212gnfgcwce4di8qzcg.png)