The problem states that $P = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$, $T = \begin{pmatrix} -3 \\ 1 \end{pmatrix}$, and $TOP = (x,y) = (6, -6)$. We are asked to find the values of $x$ and $y$.

1. Problem Description

The problem states that $P = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$, $T = \begin{pmatrix} -3 \\ 1 \end{pmatrix}$, and $TOP = (x,y) = (6, -6)$. We are asked to find the values of $x$ and $y$.

2. Solution Steps

The problem states that $(x, y) = (6, -6)$. We want to find the values of $x$ and $y$.

Since we are given that $(x, y) = (6, -6)$, we can equate the corresponding components.

$x = 6$

$y = -6$

There seems to be a typo in the image. It looks like $(x,y)=(6t,-6t)$.

But TOP=(6,-6) is given, therefore $x=6$ and $y=-6$.

3. Final Answer

$x=6$ and $y=-6$.