System A:
Notice that:
[tex]-(-x+5y)=x-5y,[/tex]
therefore the first system of equations implies that:
[tex]-5=5,[/tex]
the above result is a contradiction, therefore system A has no solution.
System B:
Notice that:
[tex]-(-x+2y)=x-2y,[/tex]
therefore the second system of equations implies that:
[tex]6=6,[/tex]
then the second system has infinitely many solutions, they must satisfy:
[tex]y=\frac{x}{2}-3.[/tex]
Answer:
System A: The system has no solution.
System B: The system has infinitely many solutions, they must satisfy:
[tex]y=\frac{x}{2}-3.[/tex]
