Question

Show that the lines x-y-2=0, x + y - 4=0, x + 3y - 6 = 0 are concurrent.​

Answer 1

Given:

There equation of line which are x-y-2=0, x + y - 4=0 and x + 3y - 6 = 0.

To Find :

Prove that they are concurrent.

Solution:

Equation of line are:

X- Y = 2         ...1)

X + Y = 4       ...2)

X + 3Y = 6    ...3)

On adding equation 1) and equation 2), we get:

X+ X  = 2 + 4

2X = 6

X = 3

On putting the value of X in equation 1):

X- Y  = 2

3 - Y = 2

-Y = 2 -3

-Y = -1

Y = 1

On putting value of X and Y in L.H.S of equation 3):

X + 3Y = 6

L.H.S

X + 3 Y

3 + 3×1

3+3

6 = R.H.S

Means intersection of line 1 and line 2 are lie on line 3. So all three line are concurrent. Means these are intersect at a common point.