7.2 Two-Variable Linear Systems

Elimination method

Solve for (x, y)

Given the System, I want to reduce the number of variables. By multiplying both sides of each equation by a number, we can have opposite coefficients to add together to eliminate a variable.

50562023

yxyx

Solve for (x, y)

Given 5056505615056

4046 202322023

yxyxyxyxyxyx

10

10

y

y

Solve for (x, y)

Given 5056505615056

4046 202322023

yxyxyxyxyxyx

10

10

y

y

Now to find x replace y with 10, in either equation

Solve for (x, y)

Given 5056505615056

4046 202322023

yxyxyxyxyxyx

10 10

yy

003

20203201023

xxxx

10,0

Airplane SpeedAn airplane flying into a headwind travels

the 1800-mile flying distance between Pittsburgh, Pennsylvania and Phoenix, Arizona in 3 hour hours and 36 minutes. On the return flight, the distance is traveled in 3 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

Airplane SpeedAirplane travels the 1800-mile in 3 hour

hours and 36 minutes. Return the same distance in 3 hours.

Find the airspeed, speed of the wind, both constant. Write variable for Speeds

Airplane speed r

Wind speed w

Airplane SpeedAirplane travels the 1800-mile in 3 hour

hours and 36 minutes. Return the same distance in 3 hours.

Airplane speed r

Wind speed w

1800)3(

180060363

wr

wr

Airplane Speed

1800)3(

180060363

wr

wr

3

18001800)3(

6.3180018006.3

wrwr

wrwr

Airplane Speed

1800)3(

180060363

wr

wr

600 1800)3(

50018006.3

wrwrwrwr

550 11002

rr

Airplane Speed 600

500

wrwr

550 11002

rr

50 600550

ww

Homework

Page 495 -498 # 4, 16, 24, 32,

40, 48, 49, 63, 74, 80

Homework

Page 495 -498 # 12, 20, 28, 36, 44, 52, 67, 76, 82