Math, asked by hemalathaauma815, 8 months ago

3x+ky-9 = 0 and x+2y-3=0 then value to K is

Answers

Answered by AlluringNightingale
3

Answer:

k = 6

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 equations are ;

3x + ky - 9 = 0

x + 2y - 3 = 0

Clearly ,

a = 3 , b = k , c = -9

a' = 1 , b = 2 , c = -3

Now,

a/a' = 3/1 = 03

b/b' = k/2

c/c' = -9/-3 = 3

Now,

We know that , for Infinitely many solution ;

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

=> 3 = k/2 = 3

=> k/2 = 3

=> k = 3×2

=> k = 6

Hence , k = 6


kaushik05: perfect
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