if the lines given by 3x +3ky=2 and 2x+5y+1=0 are parellel find the value od k
Answers
Answer :
k = 5/2
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 ;
3x + 3ky = 2
2x + 5y + 1 = 0
The given linear equations can be rewritten in there general forms as ;
3x + 3ky - 2 = 0
2x + 5y + 1 = 0
Clearly ,
a = 3
a' = 2
b = 3k
b' = 5
c = -2
c' = 1
Now ,
a/a' = 3/2
b/b' = 3k/5
c/c' = -2/1 = -2
The given lines will be parallel if ;
a/a' = b/b' ≠ c/c'
Clearly ,
a/a' ( = 3/2 ) ≠ c/c' ( = -2)
Thus ,
The lines will be parallel if ;
=> a/a' = b/b'
=> 3/2 = 3k/5
=> k = (3/2) × (5/3)
=> k = 5/2