Why did Jacobs family go to Egypt?

Answer 1

Jacob, son of Isaac, was the last of the Hebrew Patriarchs (Talmud, Berakhot 16b). He spent a lot of time in the tents (Genesis 25:27) studying his ancestors' teachings (Rashi commentary, ibid.); and eventually, like Abraham and Isaac before him, attained prophecy, in which God confirmed His covenant and promised His protection (Genesis 28:10-15).

When the opportunity presented itself, Jacob asked his elder twin brother Esau to sell him his birthright (Genesis 25:29:34), since he sensed that Esau wasn't pious enough to fully deserve it. Thus began the fulfillment of the prophecy which Rebecca had heard, that Jacob would become the dominant of her two sons (Genesis 25:22-23).

Jacob's life was replete with tribulations (Rashi commentary, Genesis 43:14). He managed to come out ahead despite the wiles of the deceitful Laban (Genesis 29:25 and 31:41) and the danger presented by the angry Esau (Genesis 27:41 and 32:12).

There were painful events with his daughter Dinah (Genesis 34:1-7) and with his being separated for two decades from his beloved son, Joseph (Genesis ch.37); and his wife Rachel died at a young age in childbirth (Genesis 35:16-19).

These troubles were a portent for the tribulations of the Jews in their times of exile. But Jacob received God's affirmation of His covenant and blessing (Genesis 28:13-14; 35:9-12; 46:2-4), signifying that the exile would eventually end. God gave Jacob the honor-title of Israel, indicating his eventual ascendancy (Genesis ch.35).

Your second question:

Jacob took the Israelites to Egypt because of famine (Genesis ch.46).It was part of God's plan, since Egypt would be the "iron furnace" (Deuteronomy 4:20) in which the Israelites would be smelted, removing the dross, and would grow into a nation ready to receive God's Torah.

See also:

Timeline

The Exodus

Answer 2

Because there was famine in their home country.