If the lines given by 3x+2ky=2 and 6x+8y=4 are coincide , then the value of k is
Answers
Answer :
k = 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 + 2ky = 2
6x + 8y = 4
The given linear equations can be rewritten in there general form as ;
3x + 2ky - 2 = 0
6x + 8y - 4 = 0
Clearly ,
a = 3
a' = 6
b = 2k
b' = 8
c = -2
c' = -4
Now ,
a/a' = 3/6 = 1/2
b/b' = 2k/8 = k/4
c/c' = -2/-4 = 1/2
The given lines will coincide each other if → a/a' = b/b' = c/c'
→ 1/2 = k/4 = 1/2
→ k/4 = 1/2
→ k = ½ × 4
→ k = 4/2
→ k = 2