Beginning Algebra, 11th Edition

Summary Exercises on Solving Systems of Linear Equations^271

Concept Check Use the preceding guidelines to solve each problem.

1.To minimize the amount of work required, tell whether you would use the substitution

or elimination method to solve each system, and why. Do not actually solve.

(a)

y= 4 x

3 x+ 5 y= 69 (b)

x-y=- 5

3 x+y=- 7 (c)

9 x+ 8 y= 7

3 x- 2 y= 0

2.Which system would be easier to solve with the substitution method? Why?

System A: System B:

In Exercises 3 and 4, (a)solve the system by the elimination method, (b)solve the system

by the substitution method, and (c)tell which method you prefer for that particular system

and why.

3. 
   
   
   
   4. 
      
   
   
   
   

Solve each system by the method of your choice. (For Exercises 5 – 7, see your answers to

Exercise 1.)

x+ 3 y= 13 x=- 3 y+ 1

4 x- 3 y=- 8 2 x+ 5 y= 0

2 x+ 8 y= 3 y=- 3 x+ 1

5 x- 3 y= 7 7 x+ 2 y= 4

5. 6. 7.

9 x+ 8 y= 7

3 x- 2 y= 0

x-y=- 5

3 x+y=- 7

y= 4 x

3 x+ 5 y= 69

11. 12. 13.

5 y= 5 - 3 x

5 x= 7 + 2 y

2 x+ 3 y= 30

3 x- 5 y= 7

• 10 x+ 15 y=- 25

4 x- 6 y= 10

8. 9. 10.

y= 11 x

6 x-y= 5

5 x+ 8 y=- 1

6 x+ 7 y= 4

x=- 3 - y

x+y= 7

14. 15. 16.

• 3 x+ y= 18

2 x+ 3 y= 10

• 4 x+ 6 y= 14

2 x- 3 y= 7

3 x+ 2 y= 2

4 x+ 3 y= 1

17. 18. 19.

3 x= 2 y

7 x- 4 y= 0

4 x+ y= 5

x- 3 y= 7

x+ y=- 1

2 x+ 5 y= 4

Solve each system by any method. First clear all fractions or decimals.

20. 
    
    
    
    21. 
        
    
    
    
    

-

1

2

x-

1

3

y=- 8

1

6

x+

1

6

y= 2

3 x- y= 9

1

5

x+

2

3

y=-

8

5

22. 23.

x

5

-

y

4

= 5

x

2

-

y

3

= 9

x

6

+

y

8

=

3

4

x

3

-

3 y

4

=-

1

2

24. 25.

0.3x-0.2y=0.9

0.2x-0.3y=0.1

0.6x+0.5y=-1.4

0.1x+ y=1.6