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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.

The author is associated with Mathematics Problem Solving Services. The author will assist you with Qualified Mathematicians.