for what value of k will the pain of lineal equation have infinite mang solutions. kx+3y=k-3 12x+ky=k
Answers
Answer:
Total no. of coins in the piggy is 180
Solution(i):
No. of 50p coins in piggy is 100
Let E be the event of drawing a coin from piggy
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
180
100
=
9
5
Therefore,Probability that a 50p coin wins =
9
5
Solution(ii):
No. of coins with value >Rs. 1 in piggy is 30
Let E be the event of drawing a coin from piggy
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
180
30
=
6
1
Therefore,Probability that a coin with value >Rs.1 falls =
6
1
Solution(iii):
No. of coins with value <Rs 5 in piggy is 170
Let E be the event of drawing a coin from piggy
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
180
170
=
18
17
Therefore,Probability that a coin with value <Rs.5 falls =
18
17
Solution(iv):
No. of Rs. 1 and Rs. 2 coins in piggy is 70
Let E be the event of drawing a coin from piggy
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
180
70
=
18
7
Therefore,Probability that a Rs. 1 and Rs. 2 coin falls =
18
7
Answer:
Given
kx+3y−(k−3)=0
Comparing with a
1
x+b
1
y+c1=0
∴a
1
=k, b
1
=3, c=−(k−3)
12x+ky−k=0
Comparing with a
1
x+b
1
y+c1=0
∴a
1
=12, b
1
=k, c=−k
Since equation has infinite number of solutions
So,
a
2
a
1
=
b
2
b
1
=
c
2
c
1
12
k
=
k
3
=
k
k−3
12
k
=
k
3
k
2
=12×3
k
2
=36
k=±6
k
3
=
k
k−3
3k=k(k−3)
3k=k
2
−3k
k
2
−3k−3k=0
k
2
−6k=0
k(k−6)=0
k=0,6
Therefore, k=6 satisfies both equations
Hence, k=6