point of intersection of linesthe lines are y= 2x - 1 and y= 1 - 4x

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to test if the given lines are concurrent, hence, you need to evaluate the solution to the given simultaneous equations, such that:

`{(y = 2x - 1),(y = 1 - 4x):}`

Replacing `2x - 1` for `y` in bottom equation yields:

`2x - 1 = 1 - 4x => 2x + 4x - 1 - 1 = 0 => 6x - 2 = 0 => 3x - 1 = 0 => 3x = 1 => x = 1/3`

Replacing back `1/3` for `x` in `y = 2x - 1` yields:

`y = 2/3 - 1 => y = (2 - 3)/3 => y = -1/3`

Hence, testing if the lines intersect each other yields that the given lines are concurrent at `x = 1/3, y = -1/3.`

 

giorgiana1976 | Student

The intercepting point of 2 lines is the point that stays on both lines same time.

In order to find out the coordinates of the intercepting point, we'll have to solve the system of equations of the lines.

y=2x-1 (1)

y=-4x+1 (2)

We'll equate (1) and (2):

2x-1=-4x+1

We'll move all terms in x to the left side and the numbers alone, to the right side.

2x+4x=1+1

We'll combine like terms:

6x=2

x=1/3

Now, we'll substitute x in any of the given equations:

y=2x-1

y=2*1/3-1

y=-1/3

The coordinates of the intercepting point are:(1/3,-1/3).