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Day Two of 7.3
Solve:

4   2         2     1
  x   y 14      y     x   11
5   5         5     5
EXAMPLE 4     Write and solve a linear system
                                P. 446 in book
 KAYAKING
 During a kayaking trip, a kayaker travels 12 miles
 upstream (against the current) and 12 miles
 downstream (with the current), as shown.The speed of
 the current remained constant during the trip. Find the
 average speed of the kayak in still water and the
 speed of the current.
EXAMPLE 4      Write and solve a linear system


 STEP 1
 Write a system of equations. First find the speed of
 the kayak going upstream and the speed of the kayak
 going downstream.

 Upstream: d = rt      Downstream: d = rt

          12 = r 3                   12 = r 2

            4=r                       6=r
EXAMPLE 4         Write and solve a linear system

 Use the speeds to write a linear system. Let x be the
 average speed of the kayak in still water, and let y be
 the speed of the current.

 Equation 1: Going upstream




              x           –      y     =            4
EXAMPLE 4       Write and solve a linear system

 Equation 2: Going downstream




            x         +      y      =             6
EXAMPLE 4      Write and solve a linear system

 STEP 2

 Solve the system of equations.

           x – y= 4                     Write Equation 1.

          x+y=6                          Write Equation 2.


          2x   = 10                      Add equations.

               x=5                      Solve for x.

 Substitute 5 for x in Equation 2 and solve for y.
EXAMPLE 4    Write and solve a linear system


       5+y=6                  Substitute 5 for x in Equation 2.

            y=1               Subtract 5 from each side.
Rectangle: P = 24 ft
Twice the length is equal
to one less than three
times the width.
Find the l & w
• #40 set up for today – oil change
Assignment: P. 448
                24-27, 35, 39-40
           #42 (A-only) EC – with work

Quiz on tomorrow over 7.1 – 7.3
 STUDY!!!

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7 3 by linear combinations - day 2

  • 1. Day Two of 7.3 Solve: 4 2 2 1 x y 14 y x 11 5 5 5 5
  • 2. EXAMPLE 4 Write and solve a linear system P. 446 in book KAYAKING During a kayaking trip, a kayaker travels 12 miles upstream (against the current) and 12 miles downstream (with the current), as shown.The speed of the current remained constant during the trip. Find the average speed of the kayak in still water and the speed of the current.
  • 3. EXAMPLE 4 Write and solve a linear system STEP 1 Write a system of equations. First find the speed of the kayak going upstream and the speed of the kayak going downstream. Upstream: d = rt Downstream: d = rt 12 = r 3 12 = r 2 4=r 6=r
  • 4. EXAMPLE 4 Write and solve a linear system Use the speeds to write a linear system. Let x be the average speed of the kayak in still water, and let y be the speed of the current. Equation 1: Going upstream x – y = 4
  • 5. EXAMPLE 4 Write and solve a linear system Equation 2: Going downstream x + y = 6
  • 6. EXAMPLE 4 Write and solve a linear system STEP 2 Solve the system of equations. x – y= 4 Write Equation 1. x+y=6 Write Equation 2. 2x = 10 Add equations. x=5 Solve for x. Substitute 5 for x in Equation 2 and solve for y.
  • 7. EXAMPLE 4 Write and solve a linear system 5+y=6 Substitute 5 for x in Equation 2. y=1 Subtract 5 from each side.
  • 8. Rectangle: P = 24 ft Twice the length is equal to one less than three times the width. Find the l & w
  • 9. • #40 set up for today – oil change
  • 10. Assignment: P. 448 24-27, 35, 39-40 #42 (A-only) EC – with work Quiz on tomorrow over 7.1 – 7.3 STUDY!!!