Cindy has $50.00 to spend on robotics kits and chemistry sets. Each robotics kit (denoted as $y$) costs $10.00, and each chemistry set (denoted as $x$) costs $8.00. We want to find a viable solution for the number of kits and sets she can purchase, assuming she spends the entire $50.

The total cost of the items she buys is represented by the equation:

$10y + 8x = 50$

Now let's analyze each option:

Option A: $(5, 1)$

Here, $y = 5$ (robotics kits) and $x = 1$ (chemistry sets). 10(5) + 8(1) = 50 + 8 = 58 \quad (\text{not viable since it exceeds $50})

Option B: $(3, 2.6)$

Here, $y = 3$ (robotics kits) and $x = 2.6$ (chemistry sets). 10(3) + 8(2.6) = 30 + 20.8 = 50.8 \quad (\text{not viable since it exceeds $50})

Option C: $(0, 5)$

Here, $y = 0$ (robotics kits) and $x = 5$ (chemistry sets). 10(0) + 8(5) = 0 + 40 = 40 \quad (\text{not viable since it's less than $50})

Option D: $(-5, 9)$

Here, $y = -5$ (robotics kits) and $x = 9$ (chemistry sets). $10(-5) + 8(9) = -50 + 72 = 22 \quad (\text{not viable since negative quantities aren't possible})$

Conclusion:

None of the given options represent a viable solution for Cindy's purchase.

Would you like more details on how to set up similar equations, or do you have any questions about this one?

Here are 5 questions related to this scenario:

1. What other combinations of $y$ and $x$ could fit the equation?
2. How would you set up the equation if each item had different prices?
3. Can Cindy buy fractional quantities of either item?
4. How would Cindy's options change if her total budget were different?
5. What if there was a discount on the robotics kits?

Tip: Always check the solution by substituting values back into the equation to verify if it satisfies the given conditions.