How are the ten commandments united?

The ten commandments are united in various ways: 

First, all ten commandments “hang” from the same main branch: God's character (Matthew 22:37-40). God is the center of all commandments, not the laws themselves. The commandments exist for His glory and delight and they are an expression of God himself (Jeremiah 9:24-26), a way to know him. Therefore, obeying all those commandments is to give testimony of him, to point to him and also to love him (John 14:21). The law, then, promotes knowledge of God and conformity to him, which leads to righteous deeds. All righteous deeds arise from love or hate of God.

Secondly, the content of each commandment overlaps that of others in such a way that all commandments interpret each other. The understanding of adultery as wrong and faithfulness as right helps us understand why idolatry is wrong, when we see it as a kind of unfaithfulness (Ezra 16, Hosea 1-3). When we understand that worshiping God only is right and act accordingly, we also understand we're not supposed to make images and worship them. Since all commandments are perspectives on the ethical life attached to the same base-principle – God's character - one can't break one commandment without breaking this base-principle and all that flows from it, that is, all the other commandments.

Thirdly, all commandments and their explicit applications form a coherent ethical system that covers all areas of life. Some of those applications are cited in detail in Scripture, addressing practical, real life situations of a given time and serving as models for our own contemporary applications (as used by the writers of the Westminster Confession of Faith and Catechisms). They're called case laws. Case laws in general and their particular subtypes (like penal laws) develop the Decalogue by expanding the range of application of a commandment. The fifth commandment, for example, teaches the overarching principle of honoring father and mother . The case law derived from it, thus, expands this principle by showing that we should also honor elders. The sixth commandment's expansion accounts for laws on self-defense, on accidental kill, on caring for other people's lives by building parapets, and so forth. The seventh commandment, when expanded, originates a whole sexual ethic. The eighth commandment is expanded by case laws on generosity, honest and hard work and providing for the poor, while the ninth is developed in such a way that it allows the legal system to function, due to the warnings against corruption. Other examples could be cited, but these will suffice.

  Finally, all ten commandments teach us to love our neighbor like God loved us (John 15:12). The whole Decalogue was summarized by Jesus in Matthew 22:37-40: “love the Lord […] and […] love your neighbor as yourself”. Only by obeying all the commandments one can perfectly love the Lord and consequently love his neighbor. But no man has ever kept the whole law except Christ. Therefore, conforming to Christ is conforming to the Law, and obeying him is obeying God's law (John 14:21; Ephesians 5:1-2). Only imitators of Christ can show true sacrificial love (Romans 15:2-3), with a heart willing to forgive, serve and suffer selflessly in humility for the sake of their neighbor.