There seems to be an apparent contradiction in the Quran concerning the slaughter of animals for purposes of consumption.
Surah 5 Al-Ma'idah, Ayat 5
Made lawful to you this day are At-Tayyibat [all kinds of Halal (lawful) foods, which Allah has made lawful (meat of slaughtered eatable animals, etc., milk products, fats, vegetables and fruits, etc.). The food (slaughtered cattle, eatable animals, etc.) of the people of the Scripture (Jews and Christians) is lawful to you and yours is lawful to them.
The last sentence allows for the consumption of food slaughtered by people of the Scripture.
Surah 6 Al-An'am, Ayat 121-121
Do not eat of (the animal) over which the name of Allah has not been pronounced (at the time of its slaughtering), for that is a transgression
This sentence quite clearly disallows for the consumption of food over which the name of Allah was not pronounced at the time of slaughtering.
This sentence contradicts the first. Jews and Christians do not follow the same practices of slaughter as muslims, in particular the utterance of the name of God/Allah is not a traditional practice. As an example, kosher meat is not required to be slaughtered under the mentioning of God's name, whether that God's name be Allah or Yahweh. Therefore, to allow the consumption of meat slaughtered by these non-muslims generally contradicts the strict command of not eating meat that has not been slaughtered under Allah's name.
What is the justification or explanation for this apparent contradiction?