Question

whithout drawing the graph, show that the following equations are of concurrent lines y=5x-3 ; y=4-2x and 2x+3y=8

Answer 1

three line concurrent means they conside at one point .
y=5x-3
5x-y-3=0

y=4-2x
2x+y-4=0

2x+3y=8

K (5x-y-3)+L (2x+y-4)+M (2x+3y-8)=0
(5K +2L+2M) x+(-K+L+3M) y+(-3K-4L-8M)=0

now,
5K+2L +2M=0
-K+L+3M=0
-3K-4L-8M=0

take determinant of coefficient of K L and M
you see determinant is zero
hence these lines are concurrent