Question

Given four lines with equations

$x+2y-3=0$
$2x+3y-4=0$
$3x+4y-5=0$
and $4x+5y-6=0$
These lines are?

• A. Concurrent
• B. The sides of a quadrilateral
• C. The sides of a parallelogram
• D. The sides of a square

Answer 1

Answer: (A)

Concurrent

Given equations of lines are
$x+2y-3=\mathrm{0...}\left(i\right)$
$2x+3y-4=\mathrm{0...}\left(ii\right)$
$3x+4y-5=\mathrm{0....}\left(iii\right)$
and $4x+5y-6=\mathrm{0....}\left(iv\right)$
On solving Eqs. (i) and (ii) we get
$x=-1,y=2$
From Eq. (iii) we get
$3(-1)+4\left(2\right)-5=0$
$\Rightarrow$ $0=0$
From Eq. (iv) we get
$4(-1)+5\left(2\right)-6=0$
$0=0$
Hence, given lines are concurrent.