X = m x 2. X representing amount of movies m being how many months.
If the smaller number is x, then the larger number has to be 20 - x in order for the arithmetic mean to be 10, as their sum must be 20.
If the geometric mean is 8 the product of the numbers has to be 64 and so the larger number is 64/x
Solving 64/x = 20 - x gives the quadratic x^2 -20x +64 = 0 so x = 4 or 16.
The two numbers are 4 and 16.
5x + y = -13.....multiply by -3
4x + 3y = -17
-----------------
-15x - 3y = 39 (result of multiplying by -3)
4x + 3y = -17
-----------------add
-11x = 22
x = -22/11
x = -2
5x + y = -13
5(-2) + y = -13
-10 + y = -13
y = -13 + 10
y = -3
solution (-2,-3)
![-20 \leq 3x+1 \leq 10\\ \Rightarrow\ -21 \leq 3x \leq 9\\ \Rightarrow\ -7 \leq x \leq 3\\ Sol=[-7\ 3]\ if\ x\ is\ a\ real. ](https://tex.z-dn.net/?f=-20%20%5Cleq%203x%2B1%20%5Cleq%2010%5C%5C%0A%5CRightarrow%5C%20-21%20%5Cleq%203x%20%5Cleq%209%5C%5C%0A%5CRightarrow%5C%20-7%20%5Cleq%20x%20%5Cleq%203%5C%5C%0A%0ASol%3D%5B-7%5C%203%5D%5C%20if%5C%20x%5C%20is%5C%20a%5C%20real.%0A)
