For this case we have the following system of equations:
![x + y = -9\\4x + y = -19](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%20-9%5C%5C4x%20%2B%20y%20%3D%20-19)
We multiply the first equation by -4:
![-4x-4y = 36](https://tex.z-dn.net/?f=-4x-4y%20%3D%2036)
We have the following equivalent system of equations:
![-4x-4y = 36\\4x + y = -19](https://tex.z-dn.net/?f=-4x-4y%20%3D%2036%5C%5C4x%20%2B%20y%20%3D%20-19)
We add the equations:
![-4x + 4x-4y + y = 36-19\\-3y = 17\\y = - \frac {17} {3}](https://tex.z-dn.net/?f=-4x%20%2B%204x-4y%20%2B%20y%20%3D%2036-19%5C%5C-3y%20%3D%2017%5C%5Cy%20%3D%20-%20%5Cfrac%20%7B17%7D%20%7B3%7D)
We find the value of the variable "x":
![x = -9-yx = -9 - (- \frac {17} {3})\\x = -9 + \frac {17} {3}\\x = \frac {-27 + 17} {3}\\x = - \frac {10} {3}](https://tex.z-dn.net/?f=x%20%3D%20-9-yx%20%3D%20-9%20-%20%28-%20%5Cfrac%20%7B17%7D%20%7B3%7D%29%5C%5Cx%20%3D%20-9%20%2B%20%5Cfrac%20%7B17%7D%20%7B3%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-27%20%2B%2017%7D%20%7B3%7D%5C%5Cx%20%3D%20-%20%5Cfrac%20%7B10%7D%20%7B3%7D)
Thus, the solution of the system is:
![(x, y): (- \frac {10} {3}, - \frac {17} {3})](https://tex.z-dn.net/?f=%28x%2C%20y%29%3A%20%28-%20%5Cfrac%20%7B10%7D%20%7B3%7D%2C%20-%20%5Cfrac%20%7B17%7D%20%7B3%7D%29)
See the graphic in the attached image
ANswer:
![(x, y): (- \frac {10} {3}, - \frac {17} {3})](https://tex.z-dn.net/?f=%28x%2C%20y%29%3A%20%28-%20%5Cfrac%20%7B10%7D%20%7B3%7D%2C%20-%20%5Cfrac%20%7B17%7D%20%7B3%7D%29)
See the graphic in the attached image
(20)(7) = 140 hours per week
(20)(365) = 7300 hours per year