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

hala718 | Certified Educator

Let d1 and d2 be two lines such that:

d1:y= 2x-1

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)

giorgiana1976 | Student

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).
The text passage contains a mathematical question about verifying the common point of intersection between two lines, and it provides a detailed solution for finding the coordinates of that point.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Given the lines y = 2x - 1 and y = - 4x +1 verify that there is a common point of the lines.

hala718 | Certified Educator

Let d1 and d2 be two lines such that:

d1:y= 2x-1

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)

giorgiana1976 | Student

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).
user
The text passage contains a mathematical question about verifying the common point of intersection between two lines, and it provides a detailed solution for finding the coordinates of that point.

TYPE: SINGLE_QUESTION_WITH_ANSWER