Beginning Algebra, 11th Edition

8.Concept Check After solving a system of linear equations by the substitution method,

a student obtained the equation “ .” He gave the solution set of the system as

WHAT WENT WRONG?

Solve each system by the substitution method.

51 0, 0 26.

0 = 0

CHAPTER 4 Review Exercises 289

9. 10. 11. 12.

x+ 3 y= 6

5 x+ 15 y= 30

x+ 2 = 2 y

4 x+ 5 y= 44

y=x+ 2

2 x- 5 y=- 19

x= 2 y

3 x+y= 7

4.3

13.Concept Check Which system does not require that we multiply one or both equations
by a constant to solve the system by the elimination method?
A.
3 x- 4 y= 4

• 4 x+ 3 y= 7

14.Concept Check For the system

(1)

(2)

if we were to multiply equation (1) by by what number would we have to multiply

equation (2) in order to

(a)eliminate the x-terms when solving by the elimination method?

(b)eliminate the y-terms when solving by the elimination method?

Solve each system by the elimination method.

- 3,

3 x+ 4 y=1,

2 x+ 12 y= 7

4.4 Solve each problem by using a system of equations.

25.The two leading pizza chains in the United States
are Pizza Hut and Domino’s Pizza. In July 2009,
Pizza Hut had 6118 more locations than Domino’s,
and together the two chains had 23,400 locations.
How many locations did each chain have? (Source:
PMQ Pizza Magazine.)

26.Two popular magazines in the United States are Reader’s Digestand People. Together,
the average paid circulation for these two magazines in 2007 was 12.9 million. The circu-
lation for Peoplewas 5.7 million less than that of Reader’s Digest. What were the
circulation figures for each magazine? (Source:Audit Bureau of Circulations.)

27.The perimeter of a rectangle is 90 m. Its length is times its width. Find the length and
width of the rectangle.

28.Laura Mancini has 20 bills, all of which are $10 or $20 bills. The total value of the money
is $330. How many of each denomination does she have?

(^1 12)

4.1– 4.3 Solve each system by any method.

15.

x+y= 8

2 x-y= 13 16.

6 x- 5 y=- 39

• 
  

  4 x+ 3 y= (^25) 17.
  6 x- 8 y= 18
  3 x- 4 y= 9 18.

  
  


• 
  

  4 x- 2 y= 6

  
  

2 x+ y= 3

19. 20. 21.

y=x- 7

x- 2 y= 5

2 x- 3 y= 0

6 x- 9 y= 0

3 x+ 4 y=- 8

2 x+ 3 y=- 5

22. 23. 24.

0.3x+0.2y=-0.5

0.4x-0.5y=-2.2

1

2

x+

2

3

y=

5

3

3

4

x-

1

3

y=

7

6

x

4

+

2 y

3

= 8

x

2

+

y

3

= 7

B.

12 x+ 24 y= 36

5 x+ 8 y= 13 C.

x- 3 y= 12

2 x+ 3 y= 5 D.

3 x- y= 6

x+ 2 y= 9