Write the value of k for which the system of equations
2x – y = 5
6x + ky = 15
has infinitely many solutions.
Answers
It has infinite solution
Therefore, a1÷a2=b1÷b2=c1÷c2
2÷6=-1÷k=-5÷-15
2k=-6
k= -6÷2
-3
Answer is -3
Given pair of system of equations :
2x – y = 5
6x + ky = 15
Solution :
The given pair of linear equation can be written as :
2x – y - 5 = 0………(1)
6x + ky - 15 = 0…………(2)
On comparing with General form of a pair of linear equations
a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 , we get :
a1 = 2, b1 = -1, c = - 5
a2 = 6 , b2 = k , c = -15
We have ,
a1/a2 = 2/6 = 1/3 , b1/b2 = -1/k & c1/c2 = -5/-15 = - 1/3
Given: A pair of linear equations has a infinitely many solutions
,then a1/a2 = b1/b2 = c1/c2
⅓ = -1/k
k = - 3
Hence, the value of k is - 3.
HOPE THIS ANSWER WILL HELP YOU……
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