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