getting texture coordinates

Hi,
I'm writing a ray tracing-engine. Now I need to calculate the texture (x, y) coordinates starting from the UV coordinates (of the triangular polygon), the (x,y,z) intersection point between eye-ray and polygon and the size of the texture (it's not a procedural one).
I know that there exist an algorithm that consists in resolving a linear equation system, but I have no good skills in these things :-)
Is there some other algorithm? Or does someone know some web tutorial/document that describes this one?
Thank you

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