A particular "system" involving equations is mostly a set or maybe bunch of equations you ought to manage in its entirety at a time. Linear equations (ones which usually graph like in a straight line lines) are usually less difficult in comparison with non-linear equations, and therefore the most straightforward linear system is usually one having a pair of equations and also a pair of parameters (Stapel, 2011). This essay seeks to create a system of linear equations from my own life.

**How Much Were Burgers Going for in the Early 90's?**

*Do You Want Fries with That?* I recently wondered what the price of fast food used to be when I was growing up. I could not come up with an accurate guess, but there is something that I vividly remember from my childhood which can help me to solve the puzzle. As a kid, I used to save money so that I can buy fries and hamburgers every Sunday as my parents were health freaks who would not allow us to eat such food. I very well remember that with 8 dollars, I could buy 2 burgers, one for Kyle the neighborhood bully to pay for 'protection' so he wouldn't tell and the other for me, and 1 packet of fries. I also remember that before Kyle came into the picture, I used to get 1 burger and 1 packet of fries at only 6 dollars. How then, can I use this information to solve my problem?

*System of Linear Equations to the Rescue.* Using the information from my case above, I can create a system of linear equations, solve the equations, and then know what the burger and the packet of fries were individually retailing at. If I take x to symbolize the burgers and y to symbolize the fries, and remembering that the total price for 2 burgers and 1 packet of fries went for 8 dollars, the resulting equation is:

2x+y=8............................. (1).

Before Kyle came into the picture, I used to get 1 burger and 1 packet of fries at 6 dollars. Using this information with x to symbolize the burger and y to symbolize the packet of fries, the resulting equation is:

x+y=6................................ (2).

We hence have a system of equations to solve:

2x+y=8

x+y=6

From (2),

x=6-y................................... (3).

We can use (3) and substitute the value of x in equation (1). With this technique, a person works out an equation for just one parameter, and after this replaces that answer within the alternative equation, and works it out (Think Quest, n.d.).

Thus,

2(6-y) +y=8

12-2y+y=8

12-y=8

y=4........................................ (4).

Substituting (4) in 2,

x+4=6

x=2.

We can thus conclude that a burger used to cost 2 dollars, while a packet of fries used to cost 4 dollars.

Conclusion

Using a bullying/extortion incident from my childhood, we can be able to deduce the exact price of a packet of fries and a burger in the early 90's. By forming a system of linear equations, we have been able to solve the equations to find out the individual prices of one packet of fries and that of one burger.

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This article was published on 2012/03/30

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## Systems of Linear Equations