I think there must be a way to solve this but I can't get there

Green + Blue = Yellow

Red + Green = Purple

Yellow - Purple = Red

Red + Green + Blue = 9

Swap out B so, R + G + Y - G = 9 R + Y = 9

And

Replace G with the provided formula R + G = P R + Y - B = P (from above) 9 -B = P 9 = P + B

but I run out of steam from then...

does anyone have any ideas.

Someone at my work says it can only be brute forced, but I don't believe this!

Are any of you smarter..

• (Put on hold because we have a rule here that puzzles not created by the poster must have full attribution -- i.e., say where they came from, so that the actual creator gets the credit they deserve. Unfortunately this produces a message saying the question is "off-topic", which of course it isn't really.) Dec 6, 2019 at 14:09
• Also, it looks to me as if this system of equations doesn't have a unique solution, unless we're supposed to make some assumptions based on the actual colours (e.g., that purple = red + blue). That doesn't seem likely, and in any case if we make all such assumptions that seem plausible the resulting system is inconsistent. Dec 6, 2019 at 15:44