Question

The given lines are

$2x+y=6;x+2y=6;7x-4y=6$

• A. Coincident
• B. Concurrent
• C. Parallel
• D. None of these

Answer 1

The correct option is B Concurrent

Consider first two equations:
$2x+y=6$ ....(i)
$x+2y=6$ ...(ii)
Multiply equation (i) with $2$ and on subtracting both equation equations,
$4x+2y=12$
$x+2y=6$
$(-)$ $(-)$ $(-)$
______________________
$3x=6$
$\Rightarrow x=2$
Now, $2+2y=6$
$\Rightarrow y=2$
Putting $x=2$ and $y=2$ in $7x-4y=6$
$\Rightarrow 14-8=6$ ....(putting the values of $x$ and $y$)
$\Rightarrow 6=6$
Thus, these lines are concurrent, as $(2,2)$ is common point for all three lines, i.e. they intersect at a single point.