# Rich Tasks 2 and 3 Quarter 1

```Transition Program Grade 12 Quarter 1
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.