Beginning Algebra, 11th Edition

Solve each applied problem. See Sections 2.4 – 2.7.

47.As of 2009, the all-time top scorer in the National Hockey League was Wayne Gretzky.

During his NHL career, Gretsky had a total of 2857 points (goals plus assists) in regular

season play. He had 1069 more assists than goals. How many goals and how many assists

did he have? (Source: World Almanac and Book of Facts.)

48.The perimeter of a rectangle is 46 ft. The width is 7 ft less than the length. Find the width.

49.Antonnette Gibbs, a cashier, has $10-bills and $20-bills. There are 6 more tens than twen-

ties. If there are 32 bills altogether, how many of them are twenties?

50.Teresa Hodge traveled for 2 hr at a constant speed. Because of roadwork, she reduced her

speed by 7 mph for the next 2 hr. If she traveled 206 mi, what was her speed on the first

part of the trip?

PREVIEW EXERCISES

270 CHAPTER 4 Systems of Linear Equations and Inequalities

43.Line segment PQhas an equation that can be written in the form.

Using the coordinates of point Pwith and , write an equation in

the variables aand b.

44.Using the coordinates of point Qwith and , write a second

equation in the variables aand b.

45.Write the system of equations formed from the two equations in Exercises 43 and

44,and solve the system by using the elimination method.

46. (a)What is the equation of the line on which segment PQ lies?
    (b)Let in the equation from part (a), and solve for y(to two decimal
    places). How does the result compare with the actual figure of $6.88?

x= 2007

x= 2008 y=7.18

x= 2000 y=5.39

y=ax+b

SUMMARY EXERCISESon Solving Systems of Linear Equations

Guidelines for Choosing a Method to Solve a System of Linear Equations

1.If one of the equations of the system is already solved for one of the

variables, as in the following systems, the substitution method is the

better choice.

and

2.If both equations are in standard form and none of the

variables has coefficient or 1, as in the following system, the elim-

ination method is the better choice.

3.If one or both of the equations are in standard form and the coefficient

of one of the variables is or 1, as in the following systems, either

method is appropriate.

and

- 5 x+ 2 y= 4 3 x- 2 y= 8

3 x+ y=- 2 - x+ 3 y=- 4

- 1

- 2 x+ 3 y= 4

4 x- 11 y= 3

- 1

Ax+By=C

y= 2 x- 6 x= 3 y- 7

3 x+ 4 y= 9 - 5 x+ 3 y= 9

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