Answer
The parallelogram with vertices $(0,0), (6,3), (12,1), (6,-2)$
Work Step by Step
In order to get the values of $u$ and $v$ we will need to solve the given two equations.
we have $u=\dfrac{x+3y}{5}; y=\dfrac{x-2y}{5}$
As we are given that $0 \leq u \leq 3$ and $0 \leq v \leq 2$
Thus, we can write
$0 \leq \dfrac{x+3y}{5} \leq 3$ and $0 \leq \dfrac{x-2y}{5} \leq 2$
This gives: $0 \leq x+3y \leq 15$ and $0 \leq x-2y \leq 10$
Hence, the parallelogram has vertices $(0,0), (6,3), (12,1), (6,-2)$
