Question

show that the lines 2x + 5y = 1 , x-3y=6 and x +5y+2=0 are concurrent.

Answer 1

To show the given three lines concurrent are 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 we 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.

Answer 2

To show the given three lines concurrent are 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 we 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.

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