Question

Check whether 2x+5y=11,4x+10y=14 is consistent or inconsistent if consistent then solve for x and y

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 ;

2x + 5y = 11 , ie ; 2x + 5y - 11 = 0

4x + 10y = 14 , ie ; 4x + 10y - 14 = 0

Clearly , we have ;

a = 2

a' = 4

b = 5

b' = 10

c = -11

c' = -14

Now,

a/a' = 2/4 = 1/2

b/b' = 5/10 = 1/2

c/c' = -11/-14 = 11/14

Clearly,

a/a' = b/b' ≠ c/c'

Thus,

Both the lines parallel and hence they are inconsistent.

Hence,

The given lines are inconsistent.