Question

Given the four lines with the equations
$\begin{array}{c}x+2y-3=0,3x+4y-7=0\\ 2x+3y-4=0,4x+5y-6=0\end{array}$
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 A they are all concurrent

The point of intersection of $x-2y-3=0$ and $2x+3y-4=0$ is $(-1,2)$

$2x+2y-6=0$

$\underset{–}{2x+3y-4=0}$

$y-2=0$

$y=2$ then $x=-1$

$(-1,2)$ is point of intersection

This point satisfies $x+5y-6=0$ and $3x+4y-7=0$

Therefore $4$ given lines are concurrent.