To solve for $x$ and $y$ when $t = 1$, using the given parametric equations:

1. $y = 3t - t^2$
2. $x = 3t^2$

Substitute $t = 1$ into both equations:

For $y$:

$y = 3(1) - (1)^2 = 3 - 1 = 2$

For $x$:

$x = 3(1)^2 = 3(1) = 3$

Thus, at $t = 1$, the values of $x$ and $y$ are: $x = 3, \quad y = 2$

Would you like a more detailed explanation or have any questions?

Here are 5 related questions:

1. What are parametric equations, and how do they differ from standard equations?
2. How do you find the derivative of $y = 3t - t^2$ with respect to $t$?
3. How would you graph the parametric curve defined by $y = 3t - t^2$ and $x = 3t^2$?
4. What happens to $x$ and $y$ as $t$ increases or decreases from 1?
5. How can you eliminate $t$ to express $y$ as a function of $x$?

Tip: Parametric equations are especially useful in describing the motion of objects, as both $x$ and $y$ depend on a third variable (often time, $t$).