Given the lines y = 2x - 1 and y = - 4x +1 verify that there is a common point of the lines.
Let d1 and d2 be two lines such that:
d2:y= -4x +1
Both lines have a common point (point of intersection) when d1=d2
==> 2x -1 = -4x + 1
==> 6x = 2
==> x= 2/6 = 1/3
==> y= 2x-1 = 2(1/3) -1 = -1/3
==> y= -1/3
Then the common point for d1 and d2 is (1/3, -1/3)
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:
We'll put (1) = (2)
We'll isolate x to the left side. For this reason, we'll add 4x and 1 both sides:
We'll combine like terms:
We'll divide by 6:
We'll substitute the value of x in(1):
So, the coordinates of the common point are: (1/3,-1/3).