Question

Is the pair of equations consistent
x+2y-4=0
2x+4y -2=0​

Answer 1

Answer:

No

Note:

★ Two lines are said to be consistent if they are either intersecting or coincident .

★ Two lines are said to be inconsistent if they are parallel .

★ Let's consider two lines ax + by + c = 0 and a'x + b'y + c' = 0 , then ;

• They are intersecting if a/a' ≠ b/b' .

• They are coincident if a/a' = b/b' = c/c' .

• They are parallel if a/a' = b/b' ≠ c/c' .

Solution:

Here,

The given equations are :

x + 2y - 4 = 0

2x + 4y - 2 = 0

Clearly,

a = 1

a' = 2

b = 2

b' = 4

c = -4

c' = -2

Now,

a/a' = 1/2

b/b' = 2/4 = 1/2

c/c' = -4/-2 = 2

Clearly,

a/a' = b/b' ≠ c/c'

Thus,

The lines are parallel and hence they are inconsistent.

Hence,

The given lines are not consistent .

( ie ; they are inconsistent ) .