You have the following equation:
[tex]\begin{gathered} 2x-9y=1 \\ x+8y=6 \end{gathered}[/tex]in order to determine which is the relation in between the previous lines, first sove each equation for y, as follow:
[tex]\begin{gathered} 2x-9y=1 \\ -9y=-2x+1 \\ y=\frac{2}{9}x-\frac{1}{9} \end{gathered}[/tex][tex]\begin{gathered} x+8y=6 \\ 8y=-x+6 \\ y=-\frac{1}{8}x+\frac{6}{8} \end{gathered}[/tex]Consider that the general form of an equation of a line is:
[tex]y=mx+b[/tex]where m is the slope anf b the y-intercept.
Take into account that the lines are parallel if they have the same slope. This is not this case.
Furthermore, consider that the lines are perpendicular if their slopes have the following relation:
[tex]m_1=-\frac{1}{m_2}[/tex]In this case, you have:
[tex]\begin{gathered} m_1=\frac{2}{9} \\ m_2=\frac{-1}{8} \\ \frac{2}{9}\ne\frac{1}{-\frac{1}{8}} \end{gathered}[/tex]As you can notice, the lines are not perpendicular.
Hence, you have that the relation between the lines is:
C. neither perpendicular nor parallel