Grade 10 Academic (MPM2D) Unit 1: Linear System Creating a System of Equations Mr. Choi © 2017 E. Choi – MPM2D - All Rights Reserved

System of Equations Many kinds of situations can be modelled using linear equations, such as manufacturing costs or economic trends. Often a problem involves two unknown quantities, which can be represented by two different variables. You may be able to write equations, using these variables, to represent the conditions described in the problem. When two or more equations are used to model a problem, it is called a system of equations. If all the equations are linear, it is called a linear system. A linear system in 2 unknowns consists of 2 or more linear equations involving 2 variables. Creating a System of Equations © 2017 E. Choi – MPM2D - All Rights Reserved

Example 1 The sum of two numbers is 255 Example 1 The sum of two numbers is 255. When the smaller is subtracted from the larger, the result is 39. Create a linear system to model this situation. You don’t need to solve it! Let x represent the smaller number. Let y represent the bigger number. Creating a System of Equations © 2017 E. Choi – MPM2D - All Rights Reserved

Example 2 Tran had $10000 to invest Example 2 Tran had $10000 to invest. She invested part of it in a term deposit paying 4% per annum and the remainder in bonds paying 5% per annum. If the total interest after one year was $440. Create a linear system to model this situation. You don’t need to solve it! Let x represent the money invested in term deposit. Let y represent the money invested in bonds. Creating a System of Equations © 2017 E. Choi – MPM2D - All Rights Reserved

Example 3 The Richmond Hill Minor Hockey Association would like to rent a banquet hall for their annual awards dinner. They have received two quotes. - Tim’s Banquet Hall charges $800 to rent the room, plus $16 for each meal. - Rock Star Palace charges $600 for the hall, plus $22 for each meal. Create a linear system to model this situation. You don’t need to solve it! Let C be the total cost of the meals in dollar Let n be the number of meals served Creating a System of Equations © 2017 E. Choi – MPM2D - All Rights Reserved

 Example 4 A riverboat took 2 h to travel 24 km down a river with the current and 3 h to make the return trip against the current. Create a linear system to model this situation. You don’t need to solve it! Let b represents the speed of the boat in still water in km/h. Let c represents the speed of the current in km/h. Recall: Creating a System of Equations © 2017 E. Choi – MPM2D - All Rights Reserved

 Example 5: (Method 1) Nick drove 500 km from Windsor to Peterborough in 5 hrs. He drove part of the way at 100 km/h, and the rest of the way at 80 km/h. Create a linear system to model this situation. You don’t need to solve it! Let x represents the distance travelled at 100 km/h. in km. Let y represents the distance travelled at 80 km/h. in km. Recall: Method 2 on next slide Creating a System of Equations © 2017 E. Choi – MPM2D - All Rights Reserved

 Example 5: (Method 2) Nick drove 500 km from Windsor to Peterborough in 5 hrs. He drove part of the way at 100 km/h, and the rest of the way at 80 km/h. Create a linear system to model this situation. You don’t need to solve it! Let x represents the time travelled at 100 km/h in hours. Let y represents the time travelled at 80 km/h in hours. Recall: Creating a System of Equations © 2017 E. Choi – MPM2D - All Rights Reserved

Homework Creating a System of Equations Work sheet: Investigation activity Text: P. 51 #7-24 P.61 #11 Check the website for updates Creating a System of Equations © 2017 E. Choi – MPM2D - All Rights Reserved

End of lesson Creating a System of Equations © 2017 E. Choi – MPM2D - All Rights Reserved