I'll leave two pictures, can someone check if I'm right? (exercise b)
2026-03-29 12:32:09.1774787529
Determine the values of a, b for which the systems have (1) exactly one solution, (2) no solutions, (3) infinitely many solutions.
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Your answer for no solution is incorrect. Note that you already found out that the system will have a unique solution iff $a\ne4$, regardless of the value of $b$. So the case $b=6,a\ne4$ gives a unique solution and has already been taken care of. You get no solution iff $a=4,b\ne6$.
The others are correct.