Given the lines y = 2x - 1 and y = - 4x +1 verify that there is a common point of the lines.

If there is a point that belongs to both lines, then this
point is the intercepting point.

In order to calculate the
coordinates of the intercepting point, we'll have to solve the system formed by the
expression of the 2 lines:

y=2x-1
(1)

y=-4x+1 (2)

We'll put (1)
= (2) 

2x-1=-4x+1

We'll
isolate x to the left side. For this reason, we'll add 4x and 1 both
sides:

2x+4x=1+1

We'll combine
like terms:

6x=2

We'll divide
by
6:

x=1/3

We'll
substitute the value of x
in(1):

y=2x-1

y=2*1/3-1

y=-1/3

So,
the coordinates of the common point are:
(1/3,-1/3).