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Given the four lines with the equations ...

Given the four lines with the equations
`x+2y-3=0`, `3x+4y-7=0`,
`2x+3y-4=0`, `4x+5y-6=0`, then

A

they are all concurrent

B

they are the sides of a quadrilateral

C

only three lines are concurrent

D

None of the above

Text Solution

Verified by Experts

Given lines, `x+2y-3=0` and `3x+4y-7=0` intersect at `(1,1)`, which does not satisfy `2x+3y-4=0` and `4x+5y-6=0`.
Also, `3x+4y-7=0` and `2x+3y-4=0` intersect at `(5,-2)` which does not satisfy `x+2y-3=0` and `4x+5y-6=0`.
Lastly, intersection point of `x+2y-3=0` and `2x+3y-4=0` is `(-1,2)` which satisfy `4x+5y-6=0`. Hence, only three lines are concurrent.
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