Find value of k for which pair of linear equations 3x +2y = -5 and x - ky = 2 has a unique solution
Answers
Answer :
k ≠ -2/3
(k can be any real no. other than -2/3)
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 equations are ;
3x + 2y = -5
x - ky = 2
The given linear equations can be rewritten in their general forms as ;
3x + 2y + 5 = 0
x - ky - 2 = 0
Clearly , we have ;
a = 3
a' = 1
b = 2
b' = -k
c = 5
c' = -2
For the given pair of linear equations to have a unique solution , a/a' ≠ b/b' .
=> 3/1 ≠ 2/-k
=> k ≠ -2/3