I will just attach a picture. Can someone help me to solve this? I think I missed some information. 
2026-03-29 12:31:52.1774787512
Determine the values of a, b and c, for which the systems have (1) exactly one solution, (2) no solutions, (3) infinitely many solutions.
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I have the same result as you: If $$a-2b+c=0$$ then we get infinity many solutions. If $$a-2b+c\ne 0$$ then we get no solutions.Since the last two equations are $$x_2+2x_3=\frac{4a-b}{3}$$ and $$x_2+2x_3=\frac{7a-c}{6}$$