We have studied several linear relations in the previous chapters

1
Lesson 5.1
2

• We have studied several linear relations in the
  previous chapters
• Height of elevators
• Wind chill
• Rope length
• Walks in front of a CRB
• In this lesson we will consider two or more
  linear equations together

3
System of Equations

• A system of equations is a set of two or more
  equations that have variables in common. The
  common variables relate similar quantities.
• You can think of a equation as a condition
  imposed on one or more variables
• The equation y 2x imposes the condition that
  every y value is twice every x value.
• A system of equations imposes several conditions
  simultaneously
• The equations y3x and y ½(x1) impose two
  conditions on y.
• Describe the two conditions imposed on y by these
  two equations.

4
Where Will They Meet?

• In this investigation you will solve a system of
  simultaneous equations to find the time and
  distance at which two walkers meet.
• Suppose that two people begin walking in the same
  direction at different average speeds.
• 1st walker starts behind the slower 2nd walker
• When and where will the faster walker overtake
  the slower walker?

5
Setting up the investigation

• Mark a 6 m segment at 1 m intervals
• Identify
• 1st Walker(starts at 0.5 meters and walks toward
  the 6 m mark at a speed of 1 m/s)
• 2nd Walker(starts at the 2 m mark and walks
  toward the 6 m mark at 0.5 m/s)
• A timekeeper (Counts 1 sec. out loud)
• A recorder (Records the time and position of each
  walker separately)
• Practice the walks

6
Collecting Data

• When each walker can follow the instruction
  accurately, record the time and position of each
  walker and the timer calls out the time.

7
Writing Equations

• Enter the data in the lists of the graphing
  calculator.
• L1 time
• L2 position of 1st walker
• L3 position of 2nd walker
• Write an equation that fits each walkers data
• Enter the equations into the graphing calculator
• Find the approximate point where the lines
  intersect.
• Explain the real-world meaning of the
  intersection point
• Check that the coordinates of the point of
  intersection satisfy both of your equations.

8
What if?

• Suppose walker A walks faster than 1 m/s.
• How is the graph different?
• What happens to the point of intersection?
• Suppose that two people walk at the same speed
  and direction from different starting marks.
• What does this graph look like?
• What happens to the solution point?
• Suppose that two people walk at the same speed in
  the same direction from the same starting mark.
• What does this graph look like?
• How many points satisfy this system of equations?

9
In this Section

• You wrote a system of two equations to model a
  real-world situation.
• You solved a system of two equations using tables
  and graphs.
• You found the meaning of the point of
  intersection in a real-world situation.

10
Confirming Points of Intersection

• Edna leaves the trailhead at dawn to hike 12 mi
  toward the lake, where her friend Maria is
  camping. At the same time, Maria starts her hike
  toward the trailhead, Edna is walking uphill so
  she averages only 1.5 mi/h, while Maria averages
  2.5 mi/hr walking downhill. When and where will
  they meet?
• Define variables for time and distance from the
  trailhead.
• Write a system of two equations to model this
  situation.
• Solve this system by creating a table and finding
  the values for the variables that make both
  equations true. Then locate this solution on a
  graph.
• Check your solution and explain its real-world
  meaning.

11
Confirming Points of Intersection

• Define variables for time and distance from the
  trailhead.
• X time walked in hours
• Y distance from trailhead in miles

12
Confirming Points of Intersection

• Write a system of two equations to model this
  situation.
• Y1.5X
• Y12-2.5X

13
Confirming Points of Intersection

• Solve this system by creating a table and finding
  the values for the variables that make both
  equations true. Then locate this solution on a
  graph.

14
Confirming Points of Intersection

• Check your solution and explain its real-world
  meaning.

15
Thinking about the exercises

• You will be assigned one problem to solve and
  then present your solution to the group.
• P. 276 1
• P. 277 2
• P. 277 3
• P. 277 4
• P. 278 6
• P. 279 11