Final answer:
The given lines are perpendicular to each other.
Step-by-step explanation:
The given pair of lines are represented by the equations x+3y=-3 and 3x-y=0.
To determine whether the lines are parallel, perpendicular, or neither, we need to compare the slopes of the lines. The given equations are in the form Ax+By=C, where A and B are the coefficients of x and y, respectively.
To find the slope of a line, we can rearrange the equation to get it in the form y=mx+b, where m is the slope and b is the y-intercept.
In the first equation, x+3y=-3, rearranging it gives 3y=-x-3, y=(-1/3)x-1. Therefore, the slope of the first line is -1/3.
In the second equation, 3x-y=0, rearranging it gives y=3x. Therefore, the slope of the second line is 3.
Since the slopes of the lines are negative reciprocals of each other (-1/3 and 3), the lines are perpendicular to each other.