3x-y-5=0 (a1=3, b1=-1,c1=-5)
6x-2y-p=0 (a2=6,b2=-2,c2=-p)

we know in parallel lines,
a1/a2 =b1/b2 is not equal to c1/c2

Identifying the Condition for Parallel Lines:
To determine the condition for two lines to be parallel, we need to look at the slopes of the lines. Two lines are parallel if their slopes are equal. The slope of a line in the form of ax + by + c = 0 is given by -a/b.

Finding the Slopes of the Given Equations:
1. The slope of the line 3x - y - 5 = 0 is -3.
2. The slope of the line 6x - 2y - p = 0 is -6/-2 = 3.

Determining the Value of p:
For the two lines to be parallel, their slopes must be equal. Since the slope of the first line is -3 and the slope of the second line is 3, we set them equal to find the value of p:
-3 = 3
-3 ≠ 3
Since -3 is not equal to 3, the two lines are not parallel. To make the lines parallel, we need to adjust the second line such that its slope matches the slope of the first line. This can be achieved by making the coefficient of y in the second equation the same as the coefficient of y in the first equation.

Therefore, the value of p that would make the lines parallel is:
p = -2*y coefficient = -2*(-1) = 2
By setting p = 2 in the equation 6x - 2y - p = 0, the lines represented by the equations 3x - y - 5 = 0 and 6x - 2y - 2 = 0 will be parallel.