Question

3х - 4y = 5, бх - 8y = 10 is consistent or not​

Answer 1

AnsWer :

Consistent.

SolutioN :

We have, Pair of Linear Equation.

3x - 4x = 5. _________ ( 1 )

6x - 8x = 10. _________ ( 2 )

Where as,

• a1 = 3.
• a2 = 6.
• b1 = - 4.
• b2 = - 8.
• c1 = 5.
• c2 = 10.

Condition : For many solution :

→ a1 / a2 = b1 / b2 = c1 / c2

→ 3 / 6 = - 4 / - 8 = 5 / 10.

→ 1 / 2 = 1 / 2 = 1 / 2.

$\rule{90}2$

Condition : For Unique solution.

→ a1 / a2 ≠ b1 / b2

→ 3 / 6 ≠ - 4 / - 8

→ 1 / 2 ≠ 1 / 2.

$\rule{90}2$

Condition : No Solution.

→ a1 / a2 = b1 / b2 ≠ c1 / c2

→ 3 / 6 = - 4 / 8 ≠ 5 / 10.

→ 1 / 2 = 1 / 2 ≠ 1 / 2.

Only, Many solution or infinite many solution condition is satisfied.

So, Lines are Coincident. ( Consistent )

$\rule{200}3$

Some MorE InformatioN :

☛ Consistent :

• Unique Solution
• a1 / a2 ≠ b1 / b2
• Lines are intersecting.

And,

• Many solution.
• a1 / a2 = b1 / b2 = c1 / c2.
• Lines are Coincident

☛ Inconsistent :

• No Solution.
• a1 / a2 = b1 / b2 ≠ c1 / c2.
• Lines are parallel.

Answer 2

Step-by-step explanation:

QUESTION :-

3х - 4y = 5, бх - 8y = 10 is consistent or not

ANSWER :-

Consistent.

We have, Pair of Linear Equation.

3x - 4x = 5. _________ ( 1 )

6x - 8x = 10. _________ ( 2 )

Where as,

a1 = 3.

a2 = 6.

b1 = - 4.

b2 = - 8.

c1 = 5.

c2 = 10.

Condition : For many solution :

→ a1 / a2 = b1 / b2 = c1 / c2

→ 3 / 6 = - 4 / - 8 = 5 / 10.

→ 1 / 2 = 1 / 2 = 1 / 2.

Condition : For Unique solution.

→ a1 / a2 ≠ b1 / b2

→ 3 / 6 ≠ - 4 / - 8

→ 1 / 2 ≠ 1 / 2.

Condition : No Solution.

→ a1 / a2 = b1 / b2 ≠ c1 / c2

→ 3 / 6 = - 4 / 8 ≠ 5 / 10.

→ 1 / 2 = 1 / 2 ≠ 1 / 2.

Only, Many solution or infinite many solution condition is satisfied.

So, Lines are Coincident. ( Consistent )