Math: Systems of Linear Equations, Coursework Example

Let X be the hours that I spend for sleep and Y be the hours that I spend surfing the internet. I get home at around 6pm and have to wake up at 6am sharp. So there’s about 12 hours in between that I can either use for sleep or surfing the internet. However, I want to make sure that I get exactly 2 hours more sleep than internet hours since getting too little sleep is bad for my health. Thus, the system of equations is as follows.

X + Y = 12

X – Y = 2

Solving for X by elimination of Y,

2X = 14

X=7

Solving for Y by substituting X

7 + Y = 12

Y = 5

Therefore, the system is consistent. I spend 7 hours sleeping and 5 hours surfing the internet.