Answer:
![(x_1,y_1) = (0,9)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%280%2C9%29)
![(x_2,y_2) = (6,3)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%286%2C3%29)
![(x_3,y_3) = (6,12)](https://tex.z-dn.net/?f=%28x_3%2Cy_3%29%20%3D%20%286%2C12%29)
Step-by-step explanation:
Given
x = hours spent on cardiovascular work
y = hours spent on weight training
From the first statement,
Each week: he spends at least 9 hours
This is represented as:
![Total \ge 9](https://tex.z-dn.net/?f=Total%20%5Cge%209)
![x + y \ge 9](https://tex.z-dn.net/?f=x%20%2B%20y%20%5Cge%209)
From the second statement,
Each week: he spends a max of 12 hours on weights
This is represented as:
![Weight \le 12](https://tex.z-dn.net/?f=Weight%20%5Cle%2012)
![y \le 12](https://tex.z-dn.net/?f=y%20%5Cle%2012)
From the third statement,
Each week: he spends a max of 6 hours on cardio works
This is represented as:
![Cardio \le 6](https://tex.z-dn.net/?f=Cardio%20%5Cle%206)
![x \le 6](https://tex.z-dn.net/?f=x%20%5Cle%206)
So, the inequalities are:
![x + y \ge 9](https://tex.z-dn.net/?f=x%20%2B%20y%20%5Cge%209)
![y \le 12](https://tex.z-dn.net/?f=y%20%5Cle%2012)
![x \le 6](https://tex.z-dn.net/?f=x%20%5Cle%206)
See attachment for the graph where the solution are also highlighted
From the attachment, the solutions are:
![(x_1,y_1) = (0,9)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%280%2C9%29)
![(x_2,y_2) = (6,3)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%286%2C3%29)
![(x_3,y_3) = (6,12)](https://tex.z-dn.net/?f=%28x_3%2Cy_3%29%20%3D%20%286%2C12%29)