1. You have the following equations:
<span>
y=−2x+5 (i)
3x−4y=2 (ii)
2. You must substitute the equation (i) into the equation (ii), as below:
</span>3x−4y=2
3x-4(−2x+5)=2
3x+8x-20=2
11x-20=2
3. Now, you must clear the variable "x":
11x=2+20
x=22/11
x=2
4. You have the value of "x", so you can find the value of "y". When you substitute x=2 into the equation (i), you obtain:
y=−2x+5
y=-2(2)+5
y=-4+5
y=1
5. Therefore, the answer is:
x=2
y=1
Principle: divide the correct possibilities by the total nr. of possibilities to find the probability.
6. P(green) = 5 / (7+5+6) = 5/18
7. P(red) = 6 / 18 = 1/3
8. P(not green) = P(red | blue) = (6+7)/18 = 13/18
9. P(HH) = 5/25 = 1/5
10. P(HT) = 16/25
11. P(NOT TT) = P(HH | HT) = (5+16)/25 = 21/25
12. P(HH | TT) = (5+4)/25 = 9/25
13. P(5) = 1/6. P(H) = 1/2. P(5 & H) = 1/6*1/2 = 1/12. If you draw all the possibilities, you'll find there are 12. One of them is 5 & Heads.
