<u>Right Answer:
</u>
<h2>Vivía
</h2>
The word <em>familia</em> (family) is a Determined Collective Noun.
The <u>Determined Collective Nouns</u> are those that carry in their meaning the nature of their components. These nouns <u>appear in singular with a plural meaning</u>, in addition, they <u>agree with the verb in singular when they constitute nominal groups according to the subject.
</u>
This is how the word <em>Familia</em> <em>(Family: a group of people with kinship relationships, whether by marriage, blood or adoption)</em> in this sentence is the 3rd person in singular.
Then, the spanish verb <em>vivir </em>(to live) in simple past is conjugated with the 3rd person singular as <em>vivía </em>(lived).
Therefore, the whole sentence is:
<h2>
La familia Vargas <u>vivía </u>en una casa bonita. </h2>
(The Vargas family lived in a nice house)
The other options are incorrect because do not match with the noun of the sentence:
<em>vivían</em> (they lived) is the conjugation with the <u>3rd person plural</u>
<em>vivíamos</em> (we lived) is the conjugation with the <u>1st person in plural
</u>
<em>vivías</em> (you lived) is the conjugation with the <u>2nd person in singular
</u>