For what value of 'k' the pair of equations x-ky=2 and 3x+2y=-50 has a unique solution?
Answers
Answer:
k ≠ -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 ;
x - ky = 2
3x + 2y = -50
The given equations can be rewritten as ;
x - ky - 2 = 0
3x + 2y + 50 = 0
Clearly ,
a = 1 , b = -k , c = -2
a' = 3 , b = 2 , c = 50
Now,
a/a' = 1/3
b/b' = -k/2
c/c' = -2/50 = -1/25
Now,
We know that , for unique solution ;
=> a/a' ≠ b/b'
=> 1/3 ≠ -k/2
=> -k/2 ≠ 1/3
=> k ≠ -2/3
Hence ,
k ≠ -2/3 ( k can be any real number other than -2/3 ) .
Answer:
Find the value of k for which the system of linear equation
x +2y = 3 and 5x + k y = -7 has unique solution