Question

Show that the lines 2x+5y=1, x-3y=6 and x+5y+2 are concurrent?

Answer 1

To show the given three lines are concurrent we solve any two equations .

2x+5y=1----------(1)
x-3y=6-------------(2)

Multiplying (1) by 1 and (2) by 2 we have
2x+5y=1
2x-6y=12

Subtracting we get, 11y=-11
or, y=-1

then, x=6+3y=6+3(-1)
=6-3=3

Now check whether the point (3,-1) satisfy the third equation or not.

x+5y+2=3+5(-1)+2
=3-5+2=0
Since the point satisfies the third equation, therefore the given three lines are concurrent.