"The process we live today is very serious."
Translation:O processo que vivemos hoje é muito grave.
Clearly the given English translation is nonsense, but "grave" would not be used with system. It is very commonly paired with "situation," actually a journalistic cliche. But processo is not static but something going on. Vivemos should be translated "we are experiencing" I think. I guess the meaning is something like "the course our lives are taking today is gravely disturbing."
I think it depends on the intent of the author. I think the intent was to describe our human condition in a negative light, in which case "grave" would be the better translation for "serious". If the situation were not negative, e.g."He is a serious student." or "Was she being serious or was she joking?" , then "sério(a)" would be appropriate.