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you can add the arrows by the rule I gave you
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or just add the components of x of the two guys
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to get the component of the sum and likewise for the y.
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I mentioned something of increasing importance only later,
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which is that you are free to pick another set of axes,
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not in the traditional x and y direction,
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but as an oblique direction.
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If you do,
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the unit vectors are called i prime and j prime,
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the components of the vector change.
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You can imagine that if a vector is viewed from an angle,
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then its components will vary with the perspective.