Often in life the commandments of God seem to rub against each other a bit. It is often hard to know what to do at times in life. It is why the bible always calls us to wisdom. Wisdom will show us the way when life becomes difficult.
For example sometimes tensions arise between keeping confidences of things others have said to us and keeping relationships with nosy people. You know you cannot break confidence and yet you cannot confront the nosy people asking inappropriate questions because they will not understand.
There is a delicate balance at times maintaining a balanced view of the law in certain situations. Much wisdom, thought, and prayer is required.
In a biblical example David, when he was on the run, ate bread that was only permitted to be eaten by the priests. He ate what he should not eat in general and did what was right.
Is the law in conflict? No. The bible is quite helpful in that it gives us levels of wisdom. You see there is much specific guidance and some of the specifics can come into tension in situations in life. That is why the bible gives overarching principles.
The overarching principles are that we are to love God with our whole heart and love our neighbor as ourselves. You see the bible summarizes our direction easily for us when life becomes difficult.
The bible spells out the details to aid us to learn. But when we need wisdom because of the stickiness of life we should first pray, but also fall back to the overarching principle of biblical ethics of love. If we truthfully act in love after prayer and careful thought we will not be far off.