Question

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

Answer 1

The correct option is C only three lines are concurrent

Here, $x+2y-3=0$ and $3x+4y-7=0$ intersect $(1,1)$,
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 $4x+5y-6=0$
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.