Question

Determine whether or not the four straight lines with equations x + 2y – 3 = 0,
3x + 4y - 7 = 0, 2x + 3y - 4= 0 and 4x + 5y - 6= 0 are concurrent.​

Answer 1

Given :  x + 2y – 3 = 0,  3x + 4y - 7 = 0, 2x + 3y - 4= 0 and 4x + 5y - 6= 0

To find : whether or not the four straight lines  are concurrent.​

Solution:

Lines will be concurrent if they all meet  at one point

x + 2y – 3 = 0   Eq1

3x + 4y - 7 = 0,   Eq2

2x + 3y - 4= 0    Eq3

4x + 5y - 6= 0    Eq4

Solving Eq 1  & Eq2

3 * Eq1 - Eq 2

=> 3x + 6y - 9  - (3x + 4y - 7) = 0

=> 2y - 2  =0

=> y = 1

x + 2 - 3 = 0

=> x = 1  

( 1 , 1) is the intersection point of 1st two lines

Lets check other two line goes through that point or not

2x + 3y - 4= 0  

=> 2(1) + 3(1) - 4 = 0

=> 1 = 0

but 1 ≠ 0

Hence 2x + 3y - 4= 0   line does not go through ( 1 , 1)

4x + 5y - 6= 0

=> 4 + 5 - 6 = 0

=> 3 = 0

but 3 ≠ 0

Hence 4x + 5y - 6= 0 line does not go through ( 1 , 1)

four straight lines are not concurrent.​

Learn more:

Draw any 3 lines that are not concurrent. Find the number of points ...

https://brainly.in/question/11758878

Find the magnitude and direction of the resultant of the concurrent ...

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Answer 2

Answer:

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Step-by-step explanation:

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