Question

X-2y=6,3x-6y=0 check these equation are consistent or not

Answer 1

Answer:

Inconsistent

Note:

If we consider two lines,

ax + by + c = 0

a'x + b'y + c' = 0

Then,

• They are said to be consistent if they intersect or coincide each other.

• They are said to be inconsistent if they are parallel.

• They intersect at a distinct point if ;

a/a' ≠ b/b'

• They coincide each other if ;

a/a' = b/b' = c/c'

• They are parallel if ;

a/a' = b/b' ≠ c/c'

Solution:

The given equations of lines are ;

3x - 6y = 0

x - 2y = 6 or x - 2y - 6 = 0

Clearly , we have ;

a = 3

a' = 1

b = -6

b' = -2

c = 0

c' = -6

Now,

a/a' = 3/1 = 3

b/b' = -6/-2 = 3

c/c' = 0/-6 = 0

Clearly,

a/a' = b/b' ≠ c/c'

Thus,

Both the lines parallel and hence they are inconsistent.

Hence,

The given lines are inconsistent

Also refer to - https://brainly.in/question/17091061#readmore