Math, asked by anasshaikh31777, 9 months ago

with reference to the pair of linear equation
8x - 12y-K=0 ; - 6x +9y-4=0, which have
infinitely many
solutions,
Answer the following
i) state the condition for infinitely many solution
ii) Find the value of k
of k

Answers

Answered by AlluringNightingale
2

Answer :

i) a/a' = b/b' = c/c'

ii) k = -16/3

Note:

★ A linear equation is two variables represent a straight line .

★ The word consistent is used for the system of equations which consists any solution .

★ The word inconsistent is used for the system of equations which doesn't consists any solution .

★ Solution of a system of equations : It refers to the possibile values of the variable which satisfy all the equations in the given system .

★ A pair of linear equations are said to be consistent if their graph ( Straight line ) either intersect or coincide each other .

★ A pair of linear equations are said to be inconsistent if their graph ( Straight line ) are parallel .

★ If we consider equations of two straight line

ax + by + c = 0 and a'x + b'y + c' = 0 , then ;

• The lines are intersecting if a/a' ≠ b/b' .

→ In this case , unique solution is found .

• The lines are coincident if

a/a' = b/b' = c/c' .

→ In this case , infinitely many solutions are found .

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

→ In this case , no solution is found .

Solution :

Here ,

The given linear equations are ;

8x - 12y - k = 0

-6x + 9y - 4 = 0

Clearly ,

a = 8

a' = -6

b = -12

b' = 9

c = -k

c' = -4

Thus ,

a/a' = 8/-6 = -4/3

b/b' = -12/9 = -4/3

c/c' = -k/-4 = k/4

★ Condition for infinitely many solutions :

a/a' = b/b' = c/c'

Thus ,

=> -4/3 = -4/3 = k/4

=> -4/3 = k/4

=> k = (-4/3) × 4

=> k = -16/3

Hence , k = -16/3

Answered by 9224676897
1

Step-by-step explanation:

Required Answer:-

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Sender's address

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Reciever's address

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Subject

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Salutation (Respected sir/ma'am)

Content

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Informal letter -

Sender's address

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Date

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Reciever's address

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Subject

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Salutation (Dear.)

Body

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