for what value of k will the equation x+2y+(11-k)=0 and 2x+ky(10+k)=0 represent coincident lines
Answers
Step-by-step explanation:
Given :-
The pair of linear equations in two variables are x+2y+(11-k)=0 and 2x+ky(10+k)=0
To find :-
For what value of k will the equation x+2y+(11-k)=0 and 2x+ky+(10+k)=0 represent coincident lines?
Solution :-
Given that
The pair of linear equations in two variables are x+2y+(11-k)=0
On comparing with a1x+b1y+c1 = 0
a1 = 1
b1 = 2
c1 = 11-k
and 2x+ky+(10+k)=0
On comparing with a2x+b2y+c2 = 0
a2 = 2
b2 = k
c2 = 10+k
We know that
The pair of linear equations in two variables are a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 representing coincident lines then a1/a2 = b1/b2 = c1/c2
=> 1/2 = 2/k = (11-k)/(10+k)
On taking 1/2 = 2/k
=> 1×k = 2×2
=> k = 4
or
On taking 1/2 = (11-k)/(10+k)
=> 1×(10+k) = 2(11-k)
=> 10+k = 22-2k
=> k+2k = 22-10
=> 3k = 12
=> k = 12/3
=> k = 4
Therefore, k = 4
Answer:-
The value of k for the given problem is 4
Used formulae:-
→The pair of linear equations in two variables are a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 representing coincident lines then a1/a2 = b1/b2 = c1/c2