2. Example
The sum of three numbers is 6. The first number plus twice the second, minus the third is 2. The first minus the second, plus three times the third is 8.
Solution
1. Introduction. Let’s label the numbers x, y, and z.
2. Body. We can translate directly as follows.
The sum of three numbers is 6.
x + y + z = 6
The first number plus twice the second, minus the third is 2.
x y – z = 2
The first minus the second, plus three times the third is 8.
x – y z = 8

3. We now have the system of three equations:
Augmented Matrix
rref
The solution is (1, 2, 3).
3. Conclusion. The three numbers are 1, 2, and 3.

4. Example (Geometry)
In triangle ABC, the measure of angle B is three times the measure of angle A. The measure of angle C is 60o greater than twice the measure of angle A. Find the measure of each angle.
Example (Investment)
Miguel receives $306 per year in simple interest from three investments totaling $ Part is invested at 8%, part at 9%, and part at 10%. There is $1900 more invested at 10% than at 9%. Find the amount invested at each rate.
Example (Cholesterol Levels)
Americans have become very conscious of their cholesterol levels. Recent studies indicate that a child’s intake of cholesterol should be no more than 300mg per day. By eating 1 egg, 1cupcake, and 1 slice of pizza, a child consumes 302 mg of cholesterol. If the child eats 2 cupcakes and 3 slices of pizza, he or she takes in 65 mg of cholesterol. By eating 2 eggs and 1 cupcake, a child consumes mg of cholesterol. How much cholesterol is in each item?