Given the line $r$ with the Cartesian equation $3x+ 2y + 7 = 0$, and the line $s$ with parametric equations:
$$ \left\{ \begin{array}{c} x=2+3t \\ y=1+3t \\ \end{array} \right. $$
with $t ∈ \mathbb{R}$. How can I find if $r$ and $s$ are parallel or incident, and in the latter case how can I find the coordinates of the intersection point? Please help me.
HINT
A possible method is to convert the second in cartesian coordinates
$$\left\{ \begin{array}{c} x=2+3t \\ y=1+3t \\ \end{array} \right.\iff y=1+x-2\iff y=x-1$$ Now consider the system
$\begin{cases}y=x-1\\3x+ 2y + 7 = 0\end{cases}\implies3x+2(x-1)+7=0\implies5x+5=0 \implies...$