Answer
$y=2-\displaystyle \frac{2}{3}x,\qquad 0 \leq x \leq 3$
Work Step by Step
Express $t$ in terms of one variable and substitute it into the other equation.
$x=3-3t\Rightarrow\quad \left[\begin{array}{ll}
t & x\\
0 & 3\\
1/3 & 2\\
1 & 0
\end{array}\right]\Rightarrow\quad 0 \leq x \leq 3$
$3t=3-x$
$t=\displaystyle \frac{3-x}{3}$
$y=2(\displaystyle \frac{3-x}{3})\Rightarrow\quad $
$ \fbox{$ y=2-\displaystyle \frac{2}{3}x, 0 \leq x \leq 3 $}$
To graph, create a table using several values for $t$, and then calculate $(x(t), y(t)),$ plotting the points as you go. Join with a smooth curve, noting the direction in which $t$ increases.
