Systems of Linear Equations SLP
Let’s consider the following situation.
My friend Bobby rides motocross. Next weekend his team conducts an important training session, 4 hours a day. Thus, they are going to buy fuel previously. The team consists of five riders. They ride equal dirtbikes, each one takes up to 5 liters of fuel per hour. A professional dirtbike has 2-stroke engine that requires gas to be mixed with oil in ratio 24:1. Oil is sold in 2 L canisters. How much gas and how many oil canisters do they need for the weekend?
The total amount of fuel:2 (days) * 4 (hours a day) * 5 (L/hr) * 5 (bikes) = 200 LLet x represent the amount of gas (L); and y – the number of oil canisters required, each one 2 L. The total fuel amount required is 200 L, thus:x + 2y = 200(1)Gas and oil are mixed in proportion 24:1, thus:x = 24 2y;x = 48y(2)Combining (1) and (2) into a linear system:;(3)Solving the system using the substitution method:50y = 200;y = 4;x = 192
A system is consistent if it has at least one set of variables’ values that satisfies every equation in the system. In other words, if we can find a solution for the system, it is consistent. Since we managed to solve (3), it is …
