Intermediate Algebra (11th edition)

10.Concept Check Make up a system that has as its only solution.

Decide whether the given ordered pair is a solution of the given system. See Example 1.

1 0, 0 2

220 CHAPTER 4 Systems of Linear Equations

11.

x+y=- 1

x-y= (^17) ; 1 8, - 92

13.

x- y= 1

3 x- 5 y=- 12

; 1 - 1, 2 2

12.

x-y= 4

x+y= (^6) ; 1 5, 1 2

14.

3 x+ 2 y= 20

2 x- y= 8

; 1 5, 2 2

Solve each system by graphing. See Example 2.

15.

• 2 x+y= 1

x+y=- 5 16.

3 x+ y= 1

x- 4 y=- 4

17.

2 x-y= 2

x+y= 4 18.

3 x-y= 6

2 x+y= 4

Solve each system by substitution. If the system is inconsistent or has dependent equations,

say so. See Examples 3–5, 8, and 9.

19.

y= 2 x

4 x+y= 6 20.

y= 5 x

2 x-y= 6 21.

y= 2 x- 1

• x- 4 y=- 14

22.

y= 4 x+ 8

• 3 x- 5 y=- 17 23.
  
  
  • 3 x+ y= 0
  
  
  
  

3 x- 4 y=- 22 24.

x+ 2 y= 0

• 3 x+ y=- 5

25.

3 - 2 y=-x

5 x- 4 y= 9 26.

4 + 7 x=-y

6 x-y=- 9 27.

x+ 2 y= 7

4 x- 5 y=- 11

28.

2 x+ 5 y= 1

3 x- y= 10 29.

x=

3

2

y

x= 3 y+ 5 30.

x=

3

4

y

x= 6 y- 2

31.

• 3 x+ y= 0

1

2

x+

1

3

y= 3 32.

5 x - y= 0

1

4

x -

1

5

y= 9

33.

4 x- 2 y= 0

y= 2 x 34.

3 x- 9 y= 0

x= 3 y

35.

5 x- 25 y= 5

x= 5 y 36.

8 x+ 2 y= 4

y=- 4 x

37.

1.5x-0.5y=5.0

y=0.5x 38.

0.5x+1.5y=26.0

y=1.4x

39.Concept Check If a system of the form

has a single solution, what must that solution be?

40.Assuming that you want to minimize the amount of work required, tell whether you would

use the substitution or elimination method to solve each system. Explain your answers.

Do not actually solve.

Cx+Dy= 0

Ax+By= 0

(a)

x-y=- 5

3 x+y=- 7 (b)

y= 11 x

6 x-y= 5 (c)

9 x+ 8 y= 7

3 x- 2 y= 0