Problem Solving with Systems & Solving Systems with Matrices

1. Problem Solving with Systems & Solving Systems with Matrices Advanced Math Topics Mrs. Mongold

2. Steps to writing a system of equations • 1. Read and re-read the problem

3. Steps to writing a system of equations • 1. Read and re-read the problem • 2. Identify what it is you are trying to solve for

4. Steps to writing a system of equations • 1. Read and re-read the problem • 2. Identify what it is you are trying to solve for • 3. Translate the words into variables

5. Steps to writing a system of equations • 1. Read and re-read the problem • 2. Identify what it is you are trying to solve for • 3. Translate the words into variables • 4. Write an equation to model all of the situations (2 variables, 2 equations, 2 situations, 3 variables, 3 equations, 3 situations)

6. Steps to writing a system of equations • 1. Read and re-read the problem • 2. Identify what it is you are trying to solve for • 3. Translate the words into variables • 4. Write an equation to model all of the situations (2 variables, 2 equations, 2 situations, 3 variables, 3 equations, 3 situations) • 5. Solve the system

7. Steps to writing a system of equations • 1. Read and re-read the problem • 2. Identify what it is you are trying to solve for • 3. Translate the words into variables • 4. Write an equation to model all of the situations (2 variables, 2 equations, 2 situations, 3 variables, 3 equations, 3 situations) • 5. Solve the system • 6. Check your solution to make sure it makes sense in terms of the problem (positive numbers where positive numbers are required)

8. Steps to writing a system of equations • 1. Read and re-read the problem • 2. Identify what it is you are trying to solve for • 3. Translate the words into variables • 4. Write an equation to model all of the situations (2 variables, 2 equations, 2 situations, 3 variables, 3 equations, 3 situations) • 5. Solve the system • 6. Check your solution to make sure it makes sense in terms of the problem (positive numbers where positive numbers are required) • 7. Write your answer in sentence form!!!

9. Using Matrices to Solve • 1. Take System of Equations and write the coefficients and constants in the form of a matrix

10. Using Matrices to Solve • 1. Take System of Equations and write the coefficients and constants in the form of a matrix • 2. Use your calculator to solve • Casio- Equations from main menu • TI- MATRX (2nd x-1 for most models)

11. Example 1 • A first number is 4 less than a second number. Four times the first number is 6 more than twice the second. Find the numbers.

12. Example 2 • Two cars leave Indianapolis, one traveling east and the other west. After 3 hours they are 297 miles apart. If one car is traveling 5 mph faster than the other, what is the speed of each?

13. Example 3 • Lynn Pike, a pharmacist, needs 70 liters of a 50% alcohol solution. She has available a 30% alcohol solution and an 80% alcohol solution. How many liters of each solution should she mix to obtain 70 liters of a 50% alcohol solution.

14. Example 4 • A manufacturing company recently purchased $3000 worth of new equipment to offer new personalized stationery to its customers. The cost of producing a package of personalized stationery is $3.00 and it is sold for $5.50. Find the number of packages that must be sold for the company to break even.

15. Example 5 • The measure of the largest angle of a triangle is 800 more than the measure of the smallest angle, and the measure of the remaining angle is 100 more than the measure of the smallest angle. Find the measure of each angle.

16. Example 6 • The measure of the largest angle of a triangle is 900 more than the measure of the smallest angle, and the measure of the remaining angle is 300 more than the measure of the smallest angle. Find the measure of each angle.