Transition Program Grade 12 Quarter 1 Rich Task 2 Lesson 2.6: Solve Linear Systems Learning Objectives Students should be able to: Create equations in two or more variables to represent relationships between quantities; Graph equations on coordinate axes with labels and scales. Solve systems of linear equations with graphs), focusing on pairs of linear equations in two variables. Prior Knowledge needed for this task Graphing linear equations; Simplifying expressions; Writing equivalent expressions; and Making tables of values from equations. 1. Lisa’s Mum each day gives her only dimes and quarters for lunch. Lunch costs $1.50. a) Write down any possible combination of quarters and dimes that can give Lisa $1.50. b) Draw a table which shows all the ways for Lisa to get enough money to buy lunch. No of Quarters No of Dimes Total c) Write a linear equation to represent the above situation. d) Draw a line on the graph below to represent the linear equation. 2. Last Monday, Lisa’s Mum gave her 9 coins for lunch. a) Draw a table which shows how many ways these 2 coin denominations can be added to make 9 coins. b) Write a linear equation to represent the above situation. c) On the same graph paper as before, draw another line to represent the linear equation. d) What is the significance of the point where the two lines cross? 3. Using your graph, determine how many dimes and quarters Lisa got last Monday. Rich Task 3 Lesson 3.6 Solve Linear Systems in three variables Junjun’s Mum gave him coins to buy the $1.50 lunch. However, the coins comprise of nickels, dimes and quarters. If the total number of quarters and dimes add up to 9 coins and the total number of quarters and nickels add up to 8 coins, determine how many quarters, dimes and nickels Junjun got from his Mom. Represent the unknown numbers of quarters, dimes and nickels as x, y and z. Write a system of equations to represent the information given.