Answer:
![x = 2 \\ y = 4](https://tex.z-dn.net/?f=x%20%3D%202%20%5C%5C%20y%20%3D%204)
Step-by-step explanation:
![2(4x - y = 4) \\ 3x + 2y = 14 \\ \\ 8x - 2y = 8 \\ 3x + 2y = 14 \\ - - - - - - - \\ 11x = 22 \\ \\ 11x = 22 \\ x = 2 \\ \\ 4x - y = 4 \\ 4(2) - y = 4 \\ 8 - y = 4 \\ y = 4](https://tex.z-dn.net/?f=2%284x%20-%20y%20%3D%204%29%20%5C%5C%20%203x%20%2B%202y%20%3D%2014%20%5C%5C%20%20%5C%5C%208x%20-%202y%20%3D%208%20%5C%5C%20%203x%20%20%2B%202y%20%3D%20%2014%20%5C%5C%20%20-%20%20-%20%20-%20%20-%20%20-%20%20-%20%20%20-%20%20%5C%5C%2011x%20%3D%2022%20%5C%5C%20%20%5C%5C%2011x%20%3D%2022%20%5C%5C%20x%20%3D%202%20%5C%5C%20%20%5C%5C%204x%20-%20y%20%3D%204%20%5C%5C%204%282%29%20-%20y%20%3D%204%20%5C%5C%208%20-%20y%20%3D%204%20%5C%5C%20y%20%3D%204)
Answer:
x
=
7
,
−
3
Step-by-step explanation:
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The sum expressed in sigma notation is
.
Solution:
Given series is 22 + 27 + 32 + 37 + 42 + 47.
Write it in the sequence form 22, 27, 32, 37, 42, 47.
First term of the sequence = 22
Common difference = 27 – 22 = 5
This is arithmetic sequence.
term of the arithmetic sequence is
![a_n=a_1+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d)
![\Rightarrow a_n=22+(n-1)5](https://tex.z-dn.net/?f=%5CRightarrow%20a_n%3D22%2B%28n-1%295)
![\Rightarrow a_n=22+5n-5](https://tex.z-dn.net/?f=%5CRightarrow%20a_n%3D22%2B5n-5)
![\Rightarrow a_n=17+5n](https://tex.z-dn.net/?f=%5CRightarrow%20a_n%3D17%2B5n)
![\Rightarrow a_n=5n+17](https://tex.z-dn.net/?f=%5CRightarrow%20a_n%3D5n%2B17)
In the given series number of terms is 6.
So n = 1 to 6.
Write n = 1 in the lower of the sigma and 6 in the top of the sigma.
![\sum_{n=1}^{6} 5 n+17](https://tex.z-dn.net/?f=%5Csum_%7Bn%3D1%7D%5E%7B6%7D%205%20n%2B17)
The sum expressed in sigma notation is
.
A) The solutions to this set of equation is where the graphs cross. They cross at point (-3, -2).
B) The solutions for f(x) would be points that fall on the graph of f(x). Two possible points are (-3, -2) and (-7, 3)
C) These 2 functions cross at (4, 1). That is the solution.