25 Did Satan carry Jesus to the Temple first

Mr. Matthew vs Mr. Luke

The Gospel of Matthew says:

That the Devil took Jesus to the Temple top first

But hold on!

The Gospel of Luke says:

That the Devil took him to a mountain top first

In Matthew, Jesus and the Devil head to a Temple top first and then to a mountain top.

The Devil sweeps Jesus away to Jerusalem’s Temple before transporting Jesus to a mountain

Matthew 4:5 Then Jesus was led by the Spirit into the desert to be tempted by the devil. 2 After fasting forty days and forty nights, he was hungry. ... 5 Then the devil took him to the holy city and had him stand on the highest point of the temple. ... 8 Again, the devil took him to a very high mountain and showed him all the kingdoms of the world and their splendor.

But Luke has it the other way around. They head to a mountain top first and then to the Temple.

The Devil transports Jesus to a mountain or high place and then carries him to the Temple

Luke 4:1 Jesus, full of the Holy Spirit, returned from the Jordan and was led by the Spirit in the desert, 2 where for forty days he was tempted by the devil. ... 5 The devil led him up to a high place and showed him in an instant all the kingdoms of the world. ... 9 The devil led him to Jerusalem and had him stand on the highest point of the temple.

Recap: Matthew tells it one way and Luke the other way. The supposedly inspired texts present different sequences and something tells me it's because they aren't inspired.