she just tried to guess the answers just like she does in the homework
This communicates your meaning effectively. Using "like" in this construction is sometimes considered a grammatical mistake, but it's a very common usage.
The rule is supposedly that "like" is a preposition, while "as" is a conjunction. As a rule of thumb, if there is a verb coming soon after the word, the correct choice is "as":
she tried to guess as she does in the homework
... while, if you are simply comparing two things, you use "like":
Her test is wrong, like her homework.
However, a usage guide at the Merriam-Webster entry on like shows that, like many grammar "rules," the objection to using "like" as a conjunction arose in the 19th century, stands in opposition to centuries of use, and should perhaps be seen as overly officious today, even if it's wise to abide by it in academic writing:
Like has been used as a conjunction in ways similar to as since the 14th century. In the 14th, 15th, and 16th centuries it was used in serious literature, but not often; in the 17th and 18th centuries it grew more frequent but less literary. It became markedly more frequent in literary use again in the 19th century. By mid-century it was coming under critical fire, but not from grammarians, oddly enough, who were wrangling over whether it could be called a preposition or not. There is no doubt that, after 600 years of use, conjunctive like is firmly established. It has been used by many prestigious literary figures of the past, though perhaps not in their most elevated works; in modern use it may be found in literature, journalism, and scholarly writing. While the present objection to it is perhaps more heated than rational, someone writing in a formal prose style may well prefer to use as, as if, such as, or an entirely different construction instead.