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Applications of Systems of Equations

Learn how to solve practical problems using systems of equations in three simple steps: naming variables, writing equations, and solving using matrices or graphing. Examples included!

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Applications of Systems of Equations

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  1. Applications of Systems of Equations

  2. Three Steps to solving applications • Step 1: NAME YOUR VARIABLES!! What are you looking for and what are you going to call them in math language? • Step 2: Write the number of equations that equals the number of variables. • Step 3: Line up variables and solve using matrices OR solve for y and graph.

  3. Example 1 • You are selling tickets at a high school football game. Student tickets cost $2, and general admission tickets cost $3. You sell 1957 tickets and collect $5035. How many of each type of ticket did you sell?

  4. Example 2 • A collection of nickels and dimes is worth $3.30. There are 42 coins in all. How many of each coin are there?

  5. Example 3 • The perimeter of a lot is 84 feet. The length exceeds the width by 16 feet. Find the length and width of the lot.

  6. Example 4 • Three solutions contain a certain acid. The first contains 10% acid, the second 30%, and the third 50%. A chemist wishes to use all three solutions to obtain a 50 – liter mixture containing 32% acid. If the chemist wants to use twice as much of the 50% solution as the 30% solution, how many liters of each solution should be used?

  7. Example 5 • The sum of two numbers is -11. Twice the first number minus the second is 32. Find the numbers.

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