Question

Check whether the following pair of linear equations are consistent or inconsistent.
6x – 4y + 10 = 0; 3x – 2y = –5​

Answer 1

Answer:

in consistent

I hope it hepl u

Answer 2

Answer:

The given pair of linear equations is consistent.

Step-by-step-explanation:

The given linear equations are

6x - 4y + 10 = 0 and 3x - 2y = - 5.

Now,

6x - 4y + 10 = 0 - - ( 1 )

Comparing with ax + by + c = 0, we get,

• a₁ = 6
• b₁ = - 4
• c₁ = 10

Now,

3x - 2y = - 5

⇒ 3x - 2y + 5 = 0 - - ( 2 )

Comparing with ax + by + c = 0, we get,

• a₂ = 3
• b₂ = - 2
• c₂ = 5

Now,

$\displaystyle{\sf\:\dfrac{a_1}{a_2}\:=\:\cancel{\dfrac{6}{3}}}$

$\displaystyle{\implies\sf\:\dfrac{a_1}{a_2}\:=\:2\:\:\:-\:-\:-\:(\:1\:)}$

Now,

$\displaystyle{\sf\:\dfrac{b_1}{b_2}\:=\:\dfrac{\cancel{-}\:4}{\cancel{-}\:2}}$

$\displaystyle{\implies\sf\:\dfrac{b_1}{b_2}\:=\:\cancel{\dfrac{4}{2}}}$

$\displaystyle{\implies\sf\:\dfrac{b_1}{b_2}\:=\:2\:\:\:-\:-\:-\:(\:2\:)}$

Now,

$\displaystyle{\sf\:\dfrac{c_1}{c_2}\:=\:\cancel{\dfrac{10}{5}}}$

$\displaystyle{\implies\sf\:\dfrac{c_1}{c_2}\:=\:2\:\:\:-\:-\:-\:(\:3\:)}$

From equations ( 1 ), ( 2 ) & ( 3 ),

$\displaystyle{\underline{\boxed{\red{\sf\:\dfrac{a_1}{a_2}\:=\:\dfrac{b_1}{b_2}\:=\:\dfrac{c_1}{c_2}}}}}$

∴ The given pair of linear equations is consistent.