Question

show that the lines x-y=6 , 4x-3y=20 and 6x +5y +8=0 are concurrent .also find their point of concurrence

Answer 1

Please see the attachment

Answer 2

∴ All equation are concurrent and the point of concurrence is $(2,-4)$

Step-by-step explanation:

Given;

$x-y=6$_equation-1, $4x-3y=20$_equation-2 and $6x+5y+8=0$_equation-3

Multiply $4$ in equation-1 and subtract with equation-2;

$4x-4y-4x+3y=24-20$

⇒$-y=4$

∴$y=-4$

This $y$ substitute in equation-1;

$x+4=6$

∴$x=2$

This $x$ and $y$ substitute in equation-3,if it is satisfied then all equation are concurrent.

So,From equation-3;

$6\times 2+5\times -4+8$

$=12-20+8$

$=0$

So, All equation are concurrent and the point of concurrence is $(2,-4)$