To continue solving the system after Marni multiplied the first equation by -2, we have the following two equations:
- \(-2x - 2y = -12\)
- \(2x + 3y = 14\)
Next, we will add these two equations together to eliminate the \(x\) variable:
\[ (-2x - 2y) + (2x + 3y) = -12 + 14 \]
This simplifies to:
\[ (-2y + 3y) = 2 \]
So, we have:
\[ y = 2 \]
Now that we have the value of \(y\), we can substitute \(y = 2\) back into the first equation to find \(x\):
\[ x + y = 6 \]
Substituting \(y\):
\[ x + 2 = 6 \]
Subtracting 2 from both sides:
\[ x = 4 \]
Thus, Marni determined that Alyssa plans to purchase:
- 4 cups of frozen fruit puree
- 2 cups of yogurt
So the final answer is: Alyssa plans to purchase 4 cups of fruit puree and 2 cups of yogurt.