To determine if two lines are parallel, perpendicular or neither we need to compare the value of their slopes. This requires that we put the equations in the general format of a line y = mx + b.
We can rearrange the first equation
x + 2y = 5
by subtracting x from both sides and then dividing by two to get
y = -(1/2) x + 5/2
so the slope of the line is -1/2 and the y-intercept is 5/2.
For the second equation, we rearrange
-2x + y = 5
by adding 2x to both sides of the equation resulting in
y = 2x + 5
This line has a slope of 2 and a y-intercept of 5.
Perpendicular lines have slopes that are the negative reciprocal of each other. The negative reciprocal of 2 is -1/2, so these lines are perpendicular.