Unit 1 – Lesson 22 Date:

Objective: Students will explore how to solve a system of equations graphically and how to verify the solution of a linear system by substitution

America is Connected by a Network of Highways

The towns, villages and cities of America are connected by a network of highways. Every winter, millions of Americans use highways like I-95 to migrate to states in the sun belt. Determining where those highways will intersect is an important part of planning their routes. The map shows that I-95 runs northwest from point C near Port St. John intersecting Highway 407 at point B. If point A is taken as the origin of a coordinate system with axes as shown, then highways I-95 and 407 are represents by lines with equations y1=-1.4x+3.9 and y2=1.6x respectively (where x and y are measured in kilometers). /

Lesson Launch:

·  What is the relationship between the first and second coordinates of a location on I-95? On Highway 407?

·  How many points of locations are on both highways?

·  Is there a location that is on both highways but is not at their intersection? How do you know?

Example #1:

To graph and solve this system of equations:

Step 1: Enter both equations into y= on the graphing calculator

Step 2: View the graph and change window, if needed, to view intersection point

Step 3: Use following commands to find intersection point:

2nd > Trace > 5: Intersect > move the pointer to the intersection point and press ENTER three times

The coordinates of the intersection point and then given on the screen

Graph the system (be sure to label your lines) and identify solution

/ Solution: ______

Step 4: Verify your solution:

Substitute your solution into the first equation y1=-1.4x+3.9 and verify that it gives you a true statement / Substitute your solution into the second equation y2=1.6x and verify that it gives you a true statement

Step 5: Summarize how you can solve a system of equations graphically

Example #2: A manufacturer of basketball shoes offers two brands: the light-weight floaters at a cost of $89.50 and the superstars at a cost of $123.99. A basketball team ordered 10 pairs at a total cost of $998.47. Determine how many pairs of each type were ordered.

Step 1: Define the variables:

x represents ______

y represents ______

Step 2: Create equations to represent problem

The team ordered a total of 10 pairs of sneakers. What could this equation look like?

The total cost of the order was $998.47. What could this equation look like, remember the floaters cost $89.50 and the superstars cost $123.99 each.

Step 3: Solve each of the above equations for y so that they are in slope – intercept form

Step 4: Enter both equations into y= on the graphing calculator

Step 5: View the graph and change window, if needed, to view intersection point

Step 6: Find intersection point:

Coordinate point of the solution is ______

This point represents what in terms of the problem?

Step 7: Verify your solution:

Substitute your solution into the first equation and verify that it gives you a true statement / Substitute your solution into the second equation and verify that it gives you a true statement