9.For what value of K, the equation 2x+3y+5 = 0 and kx+4y = 10 has unique solution: k = 8/3 k ≠ 8/3 k = 3 k ≠ 3
Answers
Answer :
2nd Option : k ≠ 8/3
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 linear equations are ;
• 2x + 3y + 5 = 0
• kx + 4y = 10 → kx + 4y - 10 = 0
Clearly , we have ;
a = 2
a' = k
b = 3
b' = 4
c = 5
c' = -10
Now ,
For the given linear equations to have an a unique solution , we have ;
=> a/a' ≠ b/b'
=> 2/k ≠ 3/4
=> 2 × (4/3) ≠ k
=> 8/3 ≠ k
=> k ≠ 8/3
Hence ,
Required answer is k ≠ 8/3 .
(2nd option)
Answer:
Given equations :-
» 2x + 3y + 5 = 0
» kx + 4y = 10
➡ kx + 4y - 10 = 0
we have to find the value of k such that the pair of equations have unique solution.
we know that, when pair of equations have unique solution,
a1/a2 ≠ b1/b2
➡ 2/k ≠ 3/5
just put any value of k so that it doesn't get equal to 3/5.
you can put 1, 2 etc.
for example, k is 2, then a1/a2 = 2/2 = 1
LHS ≠ RHS
Step-by-step explanation:
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