Answer :
Explanation
Firstly, we must solve both equations for y:
Equation 1)
[tex]\begin{gathered} 3x-2y=5, \\ 3x-2y+(2y-5)=5+(2y-5),\leftarrow\text{ additive property of equality} \\ 3x-5=2y, \\ 2y=3x-5, \\ \frac{1}{2}\cdot2y=\frac{1}{2}\cdot(3x-5),\leftarrow\text{ multiplicative property of equality} \\ y=\frac{3x}{2}-\frac{5}{2}, \\ y={\textcolor{red}{\frac{3}{2}}}x-\frac{5}{2}\text{.} \end{gathered}[/tex]Equation 2)
[tex]\begin{gathered} 6y-9x=6, \\ 6y=9x+6, \\ y=\frac{9x+6}{6}, \\ y=\frac{9x}{6}+\frac{6}{6}, \\ y=\frac{9}{6}x+1, \\ y={\textcolor{red}{\frac{3}{2}}}x+1.{} \end{gathered}[/tex]The value accompanying the variable x (after solving the equation for y!) is called the slope of the line ( in our equations, I've highlighted the slope with red color).
We say that two lines are parallel if their slopes are the same. That's what happens here.
AnswerThe given set of lines are parallel.