Answer:
the solution of the system is:
x = 1 and y = 2.
Step-by-step explanation:
I suppose that we want to solve the equation:
-6*x + 6*y = 6
6*x + 3*y = 12
To solve this, we first need to isolate one of the variables in one of the equations.
Let's isolate y in the first equation:
6*y = 6 + 6*x
y = (6 + 6*x)/6
y = 6/6 + (6*x)/6
y = 1 + x
Now we can replace this in the other equation:
6*x + 3*(1 + x) = 12
6*x + 3 + 3*x = 12
9*x + 3 = 12
9*x = 12 - 3 = 9
x = 9/9 = 1
Now that we know that x = 1, we can replace this in the equation "y = 1 + x" to find the value of y.
y = 1 + (1) = 2
Then the solution of the system is:
x = 1 and y = 2.
Answer:
0
Step-by-step explanation:
We're told that
where the last fact is due to the law of total probability:
so that 
and 
are complementary.
By definition of conditional probability, we have
We make use of the addition rule and complementary probabilities to rewrite this as
![\implies P(B)-[1-P(A\cup B)^C]=[1-P(B)]-P(A\cup B^C)](https://tex.z-dn.net/?f=%5Cimplies%20P%28B%29-%5B1-P%28A%5Ccup%20B%29%5EC%5D%3D%5B1-P%28B%29%5D-P%28A%5Ccup%20B%5EC%29)
![\implies2P(B)=2-[P(A\cup B)^C+P(A\cup B^C)]](https://tex.z-dn.net/?f=%5Cimplies2P%28B%29%3D2-%5BP%28A%5Ccup%20B%29%5EC%2BP%28A%5Ccup%20B%5EC%29%5D)
![\implies2P(B)=[1-P(A\cup B)^C]+[1-P(A\cup B^C)]](https://tex.z-dn.net/?f=%5Cimplies2P%28B%29%3D%5B1-P%28A%5Ccup%20B%29%5EC%5D%2B%5B1-P%28A%5Ccup%20B%5EC%29%5D)
By the law of total probability,
and substituting this into 
gives
![2P(B)=P(A\cup B)+[P(B)-P(A\cap B)]](https://tex.z-dn.net/?f=2P%28B%29%3DP%28A%5Ccup%20B%29%2B%5BP%28B%29-P%28A%5Ccap%20B%29%5D)
