11) For what value of k is 2x + 2y 1 point
+ 2 = 0 and 4x + ky + 8 = 0 will
have unique solution? *
a) k = 4
O b) k = 3
O c) k24
O d) k= 3
Answers
Answer :
k ≠ 4
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 ;
2x + 2y + 2 = 0
4x + ky + 8 = 0
Clearly , we have ;
a = 2
a' = 4
b = 2
b' = k
c = 2
c' = 8
For the given linear equations to have a unique solution ; a/a' ≠ b/b'
Thus ,
=> 2/4 ≠ 2/k
=> k ≠ 2×(4/2)
=> k ≠ 4
Hence ,
k be any real number but not 4 .
Answer:
As the equations have a unique solution,
a1/a2≠b1/b2
=>2/4≠2/k
=>2k≠8
=>k≠4