College Algebra 9th txtbk

434 CHAPTER 7 SYSTEMS OF EQUATIONS AND MATRICES
The solution set is given by
The check is left to the reader.
5(2s 2, 3s 1, s) | s any real number6
MATCHED PROBLEM 7
Solve:
3x 2y 4z 5
2x y 5z 2
x 6z 1
ZZZ EXPLORE-DISCUSS 3
Refer to the solution to Example 7. The given representation of the solution set is
not the only one. Which of the following is a representation of the solution set?
Justify your answer.
(A) {(t, 2 1.5t, 0.5t 1) | t any real number}
(B) {(2u 4, 2u 3, u) | u any real number}
Let y v, where v is any real number, express x and z in terms of v, and find
another representation of the solution set for Example 7.
Z Applications
Examples 8–10 illustrate the advantages of using systems of equations in solving word
problems.
EXAMPLE 8 Airspeed
An airplane makes the 2,400-mile trip from Washington, D.C. to San Francisco in 7.5 hours
and makes the return trip in 6 hours. Assuming that the plane travels at a constant airspeed
and that the wind blows at a constant rate from west to east, find the plane’s airspeed and
the wind rate.
San
Francisco
SOLUTION
2,400
miles
Washington,
D.C.
Let x represent the airspeed of the plane and let y represent the rate at which the wind is
blowing (both in miles per hour). The plane’s speed relative to the ground is determined by
combining these two rates; that is,
x y Ground speed flying east to west (airspeed wind)
x y Ground speed flying west to east (airspeed wind)
Applying the familiar formula D RT to each leg of the trip leads to the following system
of equations:
2,400 7.5(x y) Washington to San Francisco: 7.5 hr, 2,400 mi
2,400 6(x y) San Francisco to Washington: 6 hr, 2,400 mi
After simplification, we have
Add these two equations to eliminate y:
2x 720
x y 320
x y 400
x 360 mph
Airspeed