Solving Linear Systems is pretty much the same as solving any other type of problem. Don’t forget to put in a verbal model, assign labels, write an algebraic model, solve the algebraic model and definitely answer the question.
Our great teacher Mr. Ford taught us this great way to solve problems using Linear Systems. It has been proven very effective especially using the three types of methods we learned about earlier: graphing, substitution and linear combinations.

Ex.) You are the manager of a redneck’s cow farm. On Friday morning, you are going over the sales made in the past week. They show that 240 cows were sold. Heifers were sold for $66.95 and bulls were sold for $84.95. The total receipts for the two types of cows were $17, 652. Your boss doesn’t know how to keep track of things so he broke the typewriter that was keeping track of how many cows you sold. Can you find out how many of each type were sold? (Try solving this on your own before looking at the answers below the Algebraic Model.

Verbal Model: Number of Heifers + Number of Bulls = Total Number

Labels: Number of Heifers: h
Number of Bulls: b
Total Number sold: 240
Sales for Heifers: 66.95h
Sales for Bulls: 84.95b
Total Sales: 17,652

Algebraic Model: x + y = 240
66.95x + 84.95y = 17,652

Using the substitution method solve the first equation for x = 240 and substitute 240 – y into the second equation. After you simplify that you will get 18 = 1584. The solution is 152 Heifers and 88 Bulls.

Ex.) The total time for a two-member dog sledding team in a 5160 –meter relay race is 16 minutes. The first sledder on the team averages 300 meters per minute and the second sledder averages 360 meters per minute. How many minutes did the first sledder kept the baton before passing it to the second sledder?

Use the following equations to help solve this question:

Time for 1st sledder + Time for 2nd sledder = Total Time

Distance for 1st sledder + Distance for 2nd sledder = Total Distance

(Answer: 10)