Answer:
The solution of the given system of equations is (-6.667,7.667).
Step-by-step explanation:
The given equations are
...(1)
....(2)
put x=0 to find the y-intercept.
![0+y=1](https://tex.z-dn.net/?f=0%2By%3D1)
![y=1](https://tex.z-dn.net/?f=y%3D1)
Therefore y-intercept of equation (1) is (0,1).
![4(0)+y=-19](https://tex.z-dn.net/?f=4%280%29%2By%3D-19)
![y=-19](https://tex.z-dn.net/?f=y%3D-19)
Therefore y-intercept of equation (2) is (0,-19).
put y=0 to find the y-intercept.
![x+0=1](https://tex.z-dn.net/?f=x%2B0%3D1)
![x=1](https://tex.z-dn.net/?f=x%3D1)
Therefore x-intercept of equation (1) is (1,0).
put y=0 to find the y-intercept.
![4x+(0)=-19](https://tex.z-dn.net/?f=4x%2B%280%29%3D-19)
![x=-\frac{19}{4}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B19%7D%7B4%7D)
Therefore x-intercept of equation (1) is (-4.75,0).
Draw the graph of both lines by joining their x and y-intercept.
From the graph it is noticed that both the line intersect each other at (-6.667,7.667).
Therefore solution of the given system of equations is (-6.667,7.667).
Answer:
![\huge\boxed{x=8;\ y=1\to(8;\ 1)}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7Bx%3D8%3B%5C%20y%3D1%5Cto%288%3B%5C%201%29%7D)
Step-by-step explanation:
![\left\{\begin{array}{ccc}y=x-7&(1)\\5+2y=7&(2)\end{array}\right\\\\\text{Substitute (1) to (2) and solve for x:}\\\\5+2(x-7)=7\qquad\text{use the distributive property}\\\\5+(2)(x)+(2)(-7)=7\\\\5+2x-14=7\\\\2x+(5-14)=7\\\\2x-9=7\qquad\text{add 9 to both sides}\\\\2x-9+9=7+9\\\\2x=16\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{16}{2}\\\\\boxed{x=8}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dy%3Dx-7%26%281%29%5C%5C5%2B2y%3D7%26%282%29%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Ctext%7BSubstitute%20%281%29%20to%20%282%29%20and%20solve%20for%20x%3A%7D%5C%5C%5C%5C5%2B2%28x-7%29%3D7%5Cqquad%5Ctext%7Buse%20the%20distributive%20property%7D%5C%5C%5C%5C5%2B%282%29%28x%29%2B%282%29%28-7%29%3D7%5C%5C%5C%5C5%2B2x-14%3D7%5C%5C%5C%5C2x%2B%285-14%29%3D7%5C%5C%5C%5C2x-9%3D7%5Cqquad%5Ctext%7Badd%209%20to%20both%20sides%7D%5C%5C%5C%5C2x-9%2B9%3D7%2B9%5C%5C%5C%5C2x%3D16%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%202%7D%5C%5C%5C%5C%5Cdfrac%7B2x%7D%7B2%7D%3D%5Cdfrac%7B16%7D%7B2%7D%5C%5C%5C%5C%5Cboxed%7Bx%3D8%7D)
![\text{Substitute it to (1):}\\\\y=8-7\\\\\boxed{y=1}](https://tex.z-dn.net/?f=%5Ctext%7BSubstitute%20it%20to%20%281%29%3A%7D%5C%5C%5C%5Cy%3D8-7%5C%5C%5C%5C%5Cboxed%7By%3D1%7D)
2 divided by 3 is 66.7%. So the fraction would be 2/3
Answer:
⅛
Step-by-step explanation:
There are two sides of a coin which means that the profanity of getting one side of the coin is ½.
There are 14 candies in total of which 7 are red, meaning that the probability of getting a red candy is 7/14, which is the same as ½.
There are 6 sides to a die, of which 3 sides contain the odd numbers 1,3 and 5. This would mean that the probability of getting an odd number on the die is 3/6, which is the same as ½.
Now to work out the probability of getting a red candy, a heads and an odd number on the die, you have to times the probability of each together to get you final answer.
So it will be, ½×½×½=⅛
It would be the second choice or letter B - (0,12)
To get the y-intercept, set x as zero. Substitute then simplify. Negative six times negative two would equal to positive twelve.
Set: x = 0
Solution: f(x) = (0 - 6) (0 - 2)
f(x) = -6 x -2
Answer: y = 12