Answer :
To know if two lines are parallel when defined in the xy-plane is to compare the slopes.
If the slopes are equal, the lines are parallel.
In order to compare the slopes, we need to put them in the form:
[tex]y=mx+b[/tex]Then, we have for A:
[tex]\begin{gathered} 2x-y=5 \\ y=2x-5 \end{gathered}[/tex]B.
[tex]\begin{gathered} 2x+y=3 \\ y=-2x+3 \end{gathered}[/tex]C.
[tex]y=2x+3[/tex]The only lies that have the same slope, hence, they are parallel, are A and C (slope: 2).
Note: B is perpendicular to A and C as the slope of B is the slope of A but opposite sign (multiplied by -1).