7) We rearrange the second equation to compare it to the first one:
[tex]\begin{gathered} -6x+2y=18 \\ 2y=6x+18 \\ y=3x+9 \end{gathered}[/tex]The slopes are m1=1/3 and m2=3. They are not equal, nor negative reciprocals, so they are not parallel nor perpendicular. As they don't have the same slope, they will intersect.
Answer: Intersecting but not perpendicular.
8)
[tex]\begin{gathered} 2x+3y=10 \\ 3y=-2x+10 \\ y=-\frac{2}{3}x+\frac{10}{3} \end{gathered}[/tex][tex]\begin{gathered} -3x+2y=11 \\ 2y=3x+11 \\ y=\frac{3}{2}x+\frac{11}{2} \end{gathered}[/tex]The slopes are negative reciprocals:
[tex]m_1=-\frac{1}{m_2}[/tex]As the slopes are negative reciprocals, both lines are perpendicular.
Answer: Perpendicular.
