To find a viable solution for the number of robotics kits (y) and chemistry sets (x) that Cindy can purchase with her $50 winnings, we can set up the equation based on the costs:
\[ 10y + 8x = 50 \]
Now let's evaluate each of the provided options to see which ones satisfy the equation:
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For \((-5, 9)\): \[ 10(-5) + 8(9) = -50 + 72 = 22 \quad \text{(not equal to 50)} \]
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For \((0, 5)\): \[ 10(0) + 8(5) = 0 + 40 = 40 \quad \text{(not equal to 50)} \]
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For \((3, 2.6)\): \[ 10(3) + 8(2.6) = 30 + 20.8 = 50.8 \quad \text{(not equal to 50)} \]
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For \((5, 1)\): \[ 10(5) + 8(1) = 50 + 8 = 58 \quad \text{(not equal to 50)} \]
None of the provided options are correct based on the spending equation \(10y + 8x = 50\). Please verify if there was an error in the question or if more options are available, as none of them yield valid solutions within the constraints of the problem.