Question

Check if the pair of equations 2x+ 3y- 12 = 0 and 6x 9y +36=0, is consistent as not ?​

Answer 1

Answer:

The given pair of linear equations is not consistent.

Step-by-step-explanation:

The given linear equations are

2x + 3y - 12 = 0 - - - ( 1 )

6x + 9y + 36 = 0 - - - ( 2 )

Comparing equation ( 1 ) with a₁x + b₁y + c₁ = 0,

• a₁ = 2
• b₁ = 3
• c₁ = - 12

Compaeing equation ( 1 ) with a₂x + b₂y + c₂ = 0,

• a₂ = 6
• b₂ = 9
• c₂ = 36

For the pair of linear equations to be consistent,

a₁ / a₂ ≠ b₁ / b₂.

Now,

a₁ / a₂ = 2 / 6

⇒ a₁ / a₂ = 1 / 3 - - - ( 3 )

Now,

b₁ / b₂ = 3 / 9

⇒ b₁ / b₂ = 1 / 3 - - - ( 4 )

From ( 3 ) & ( 4 ),

∴ a₁ / a₂ = b₁ / b₂ = 1 / 3

As the condition a₁ / a₂ ≠ b1 / b₂ is not satisfied, the given pair of linear equations is not consistent.