Systems+of+Equations

MFM2P Home Comparison-Substitution Elimination

The basic concept: solving problems that involve two relations

Andy's Pizza sells pizza in two different ways. Plan A: $6 for the crust and cheese and then $1 per topping Plan B: $2 per topping
 * The Two-Pizza Problem**

Which plan is a better deal for 2 toppings? Which plan is a better deal for 12 toppings? When do you switch plans?

This problem can be solved using a table of values and comparing. This problem can also be solved by comparing the graphs of the costs of the two plans.
 * Graphical Method**

Let C represent the cost of the pizza in dollars. Let n represent the number of toppings.

plan A: C = n + 6 plan B: C = 2n On the graph, you can clearly see which plan is cheaper (lower) for different numbers of toppings. You change plans at the point where the two graphs meet - the **point of intersection**. The **x-coordinate** of the point of intersection tells you **when** to switch plans. The **y-coordinate** of the point of intersection tells you **what** price you pay when you switch plans.

Press: [Y=] Input equations Press: [Window] Input domain (desired x-values) and range (desired y-values) Press: [Graph] Press: [2nd] [Trace] (calc) Press: 5 (intersect) Press: [enter] [enter] [enter] Co-ordinates of the point of intersection will appear at bottom of calculator.
 * Using the graphing calculator to determine point of intersection:**