The given lines are
[tex]6x-4y=8;y=\frac{3}{2}x+6;2y=3x+5[/tex]
Convert each equation in the form
[tex]y=mx+c_{}[/tex]
Therefore it follows:
[tex]\begin{gathered} 6x-4y=8\Rightarrow y=\frac{3}{2}x+2 \\ y=\frac{3}{2}x+6\Rightarrow y=\frac{3}{2}x+6 \\ 2y=3x+5\Rightarrow y=\frac{3}{2}x+\frac{5}{2} \end{gathered}[/tex]
Therefore the slopes of all three lines are:
[tex]\begin{gathered} m_1=\frac{3}{2} \\ m_2=\frac{3}{2} \\ m_3=\frac{3}{2} \end{gathered}[/tex]
The slopes of all three lines are equal therefore all three lines are parallel with each other.
Therefore it follows that:
[tex]l_1\parallel l_2\parallel l_3[/tex]
