Question

The given lines $y=5x-3$; $y=4-2x$; and $2x+3y=8$ are

• A. coincident
• B. concurrent
• C. parallel
• D. none of these

Answer 1

The correct option is B concurrent

$y=5x-3$ ....eq1
$y=4-2x$ ....eq2
Put $y=4-2x$ in eq1
$4-2x=5x-3$
$-7x=-7$
$x=1$
Put $x=1$ in eq1 then
$y=5\times 1-3$
$y=2$
Put $x=1$ and $y=2$ in $2x+3y=8$
$L.H.S=2\times 1+3\times 2=2+6=8=R.H.S$
$\therefore$all these lines whose equation are $y=5x-3,y=4-2y,2x+3y=8$ passes through $(1,2)$.
$\therefore$ they are concurrent lines and their common point of intersection is $(1,2)$.