1) no solution
[tex]y=5x-9 \\
y=5x+9 \\ \\
5x-9=5x+9 \\
5x-5x=9+9 \\
0=18 \\
\hbox{false}[/tex]
2) one solution
[tex]y=6x+2 \\
y=3x+1 \\ \\
6x+2=3x+1 \\
6x-3x=1-2 \\
3x=-1 \\
x=-\frac{1}{3} \\ \\
y=3 \times (-\frac{1}{3})+1=-1+1=0 \\ \\
(-\frac{1}{3},0)[/tex]
3) infinitely many solutions
[tex]y=8x-2 \\
y-8x=-2 \\ \Downarrow \\
y=8x-2 \\
y=8x-2 \\ \\
8x-2=8x-2 \\
8x-8x=-2+2 \\
0=0 \\
\hbox{true}[/tex]
