Each game costs 1.25 and each ride costs 3.75
Step-by-step explanation:
Let,
Cost of each game = x
Cost of each ride = y
According to given statement;
5x+6y=28.75 Eqn 1
4x+3y=16.25 Eqn 2
Multiplying Eqn 2 by 2
![2(4x+3y=16.25)\\8x+6y=32.50\ \ \ Eqn\ 3](https://tex.z-dn.net/?f=2%284x%2B3y%3D16.25%29%5C%5C8x%2B6y%3D32.50%5C%20%5C%20%5C%20Eqn%5C%203)
Subtracting Eqn 1 from Eqn 3
![(8x+6y)-(5x+6y)=32.50-28.75\\8x+6y-5x-6y=3.75\\3x=3.75](https://tex.z-dn.net/?f=%288x%2B6y%29-%285x%2B6y%29%3D32.50-28.75%5C%5C8x%2B6y-5x-6y%3D3.75%5C%5C3x%3D3.75)
Dividing both sides by 3
![\frac{3x}{3}=\frac{3.75}{3}\\x=1.25](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B3%7D%3D%5Cfrac%7B3.75%7D%7B3%7D%5C%5Cx%3D1.25)
Putting x=1.25 in Eqn 1
![5(1.25)+6y=28.75\\6.25+6y=28.75\\6y=28.75-6.25\\6y=22.50](https://tex.z-dn.net/?f=5%281.25%29%2B6y%3D28.75%5C%5C6.25%2B6y%3D28.75%5C%5C6y%3D28.75-6.25%5C%5C6y%3D22.50)
Dividing both sides by 6
![\frac{6y}{6}=\frac{22.50}{6}\\y=3.75](https://tex.z-dn.net/?f=%5Cfrac%7B6y%7D%7B6%7D%3D%5Cfrac%7B22.50%7D%7B6%7D%5C%5Cy%3D3.75)
Each game costs 1.25 and each ride costs 3.75
Keywords: linear equation, elimination method
Learn more about elimination method at:
#LearnwithBrainly
Answer:
The average of students in the two classes who went on the field trip is
.
Step-by-step explanation:
Average = ![\frac{sum \: \: of \: \:observations }{no. \: \: of \: \:observations}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bsum%20%5C%3A%20%20%5C%3A%20of%20%5C%3A%20%20%5C%3Aobservations%20%7D%7Bno.%20%5C%3A%20%20%5C%3A%20of%20%5C%3A%20%20%5C%3Aobservations%7D%20)
Average of students in the two classes =
![\frac{ \frac{4}{5} + \frac{9}{10} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Cfrac%7B4%7D%7B5%7D%20%20%2B%20%20%5Cfrac%7B9%7D%7B10%7D%20%7D%7B2%7D%20)
![\frac{ \frac{8+9 }{ 10} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Cfrac%7B8%2B9%20%7D%7B%2010%7D%20%7D%7B2%7D%20)
![\frac{ \frac{17}{10} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Cfrac%7B17%7D%7B10%7D%20%7D%7B2%7D%20)
![\frac{17}{20}](https://tex.z-dn.net/?f=%20%5Cfrac%7B17%7D%7B20%7D%20)
Answer:
The solution to the equation system given is:
- <u>x = 2</u>
- <u>y = -1</u>
Step-by-step explanation:
First, we must know the equations given:
- 2x + 3y = 1
- 3x + y = 5
Following Crammer's Rule, we have the matrix form:
![\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
Now we solve using the determinants:
![x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%5C%5C5%261%5Cend%7Barray%7D%5Cright%5D%7D%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%7D%20%3D%5Cfrac%7B%281%2A1%29-%285%2A3%29%7D%7B%282%2A1%29-%283%2A3%29%7D%20%3D%20%5Cfrac%7B1-15%7D%7B2-9%7D%20%3D%5Cfrac%7B-14%7D%7B-7%7D%20%3D%202)
![y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%261%5C%5C3%265%5Cend%7Barray%7D%5Cright%5D%7D%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%7D%20%3D%5Cfrac%7B%282%2A5%29-%283%2A1%29%7D%7B%282%2A1%29-%283%2A3%29%7D%3D%5Cfrac%7B10-3%7D%7B2-9%7D%20%3D%5Cfrac%7B7%7D%7B-7%7D%3D-1)
Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:
- 2x + 3y = 1
- 2(2) + 3(-1)= 1
- 4 - 3 = 1
- 1 = 1
And, with the second equation:
- 3x + y = 5
- 3(2) + (-1) = 5
- 6 - 1 = 5
- 5 = 5
Answer: 123,060
So you multiply 1700 by 12 then add 110 then divide by 12 to see how much you would now pay a year, which would be 1709 (new monthly payment) then multiply that by six years 12 month's time 6 years = 72 months so multiply 1700 times 72 and you get 123060
Hope this is helpful.
The graph should look like this.