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.

5056

2023

yx

yx

Solve for (x, y)

Given

5056505615056

4046 202322023

yxyxyx

yxyxyx

10

10

y

y

Solve for (x, y)

Given

5056505615056

4046 202322023

yxyxyx

yxyxyx

10

10

y

y

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

Solve for (x, y)

Given

5056505615056

4046 202322023

yxyxyx

yxyxyx

10

10

y

y

0

03

20203

201023

x

x

x

x

10,0

Airplane Speed

An 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 Speed

Airplane 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 SpeedsAirplane speed r

Wind speed w

Airplane Speed

Airplane 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(

180060

363

wr

wr

Airplane Speed

1800)3(

180060

363

wr

wr

3

18001800)3(

6.3

180018006.3

wrwr

wrwr

Airplane Speed

1800)3(

180060

363

wr

wr

600 1800)3(

50018006.3

wrwr

wrwr

550

11002

r

r

Airplane Speed

600

500

wr

wr

550

11002

r

r

50

600550

w

w

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