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
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
Step-by-step explanation:
Required Answer:-
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Date - 18 - 2 - 2021
ABC address (receiver's address)
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What is a letter?
⟶ A letter is a form of written communication which is given to another person telling, asking or complaining about any purpose.
⟶ Letter was widely used in olden times of India. It took them few days to reach another address.
2 types of letters :-
1] Formal letter :-
Formal letters are written to any official people, like police, principal, teacher, governor, mayor, etc.
→ We use Formal language in this, and use formal greeting like respected/sincerely,etc.
2] Informal letter :-
→ Informal letters are written to your near and dear ones for eg; Uncle,aunt, brother, sister.
→ Language is always formal, like dear, etc.
Format of letter -
1. Formal letter -
Sender's address
---
Date
---
Reciever's address
---
Subject
---
Salutation (Respected sir/ma'am)
Content
---
Salutation 2 (Your sincerely)
Your name
Informal letter -
Sender's address
---
Date
---
Reciever's address
---
Subject
---
Salutation (Dear.)
Body
---
Salutation 2 (your lovingly)
Your name