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The number systems shown are Babylonian cuneiform numerals, Maya numerals, and Kaktovik numerals.
Babylonian cuneiform numerals were the first positional number system in history! They are base 60. The confusing thing about Babylonian numerals is that within each position there are up to two symbols. The sideways triangles stand for 10 each, and the downwards triangles represent 1. The breakdown for the Babylonian numerals shown here is:
More about Babylonian cuneiform numerals
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Maya numerals are base 20. Each dot stands for 1, and each bar stands for 5.
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Kaktovik numerals are a system of numerals invented by students in Kaktovik, Alaska in 1994. They are used to represent numbers from the Iñupiaq language. Like Maya numerals, they are base 20, and each numeral has a component depicting 1s and another depicting 5s. Kaktovik numerals are made up of two sets of zigzags: a more-or-less vertical zigzag on the bottom, and a more-or-less horizontal zigzag on top. Each line in the lower zigzag represents 1, and each line in the upper zigzag represents 5. The loop symbol stands for zero.
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By adding all these results together you get this puzzle's answer:
5578 + 12 + 2819 = 8409