Question

Show that the lines $3x-4y+5=0,7x-8y+5=0$ and $4x+5y=45$ are concurrent.

Answer 1

Three lives are said to be concurrent if they intersect at same point.

First we find intersection point

of line $3x-4y+5=0$....(1)

$7x-8y+5=0$....(2)

then put the point in $9x+5y=45$......(5)

if it is satisfied then lines are concurrent

$3x-4y=7x-8y$

$4y=4x$

$y=x$

$3x-4y+5=0$

$x=5,y=5$

Put in $3$

$4x+5y=4\times 5+5\times 5=45$

satisfied

Lines are concurrent.