Practice exercises 4.1
a. sketch the graph of the following linear systems. then tell whether the system is indepen-
dent, dependent or inconsistent.
1) x + y = 5
x-y=3

2) x-y=-2
2x-2y=6

3) x+2y=6
-3x-6y=-6

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

5) x+3y=6
4x-y=4

6) 2x-y=6
-4x+2y=8

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Answers

• Réponse publiée par: Rosalesdhan

  Step-by-step explanation:

  This is how you determined the graph of two equalities.

  First, be sure the same terms of equation 1 and equation 2 are on the same side.

  for example:

  x+ y =2

  2x -3y= 4

  This is good, because x and y on equation 1 and 2 are on the left side while both whole numbers on the right.

  second, make a ratio of ax, by, and c for both equationnow if :ax:by:c has the same ratio from both equation the graph is consistent-dependent.ax:by has the same ratio but different c the graph is inconsistent.totaly different ratio is consistent-indepandent.

  solve

  let's see their ratios

  1) x + y = 5 (1:1:5)

  x-y=3 (1:-1:3)

  answer : consistent-indepandent.

  2) x-y=-2 (1 : -1 : -2 )

  2x-2y=6 ( 2 : -2 : 6 ) or (1 : -1 : 3)

  answer : inconsistent

  3) x+2y=6 (1 : 2 : 6)

  -3x-6y=-6 (-3 : -6 : -6) or ( 1 : 2 : 2 )

  answer : inconsistent

  4) x+y=1 ( 1 : 1 : 1 )

  2x-3y=8 (2 : -3 : 8 )

  answer : consistent-indepandent

  5) x+3y=6 ( 1 : 3 : 6 )

  4x-y=4 (4 : -1 : 4)

  answer : consistent-indepandent

  6) 2x-y=6 ( 2 : -1 : 6 )

  -4x+2y=8 (-4 : 2 : 8 ) or ( 2 : -1 : -4 )

  answer : inconsistent

  
  
  
  
  
  
• Réponse publiée par: ian2145

  Step-by-step explanation:

  Graphs of linear system:

  Independent:  The graphs intersect.

  Different or unequal slopes (m)Different y-intercepts (b)If the product of slopes is -1, the graphs intersects and are also perpendicular to each other.

  Dependent: The graphs overlap.

  Same or equal slopes (m)Same y-intercepts (b)

  Inconsistent: The graphs are parallel.

  Same or equal slopes (m)Different y-intercepts (b)

  Change each pair of equations to slope-intercept form ⇒ y=mx + b then identify the slopes (m) and y-intercepts (b):

  1)  x + y = 5  

  y = -x + 5

  x - y=3

  y = x - 3

  Slopes (m): -1 and 1

  y- intercepts (b): 5 and -3

  System: Independent

  Graph: Intersects

  2) x - y = -2

  y = x + 2

  2x - 2y = 6

  2y/2 = 2x/2 -6/2

  y = x - 3

  Slopes (m):  1 (equal slopes)

  y- intercepts (b): 2 and -3

  System: Inconsistent

  Graph: parallel

  3) x + 2y = 6

  2y/2 = -x/2 + 6/2

  y = -x/2 + 3

  -3x - 6y = -6

  6y/6 = -3x/6 + 6/3

  y = -x/2 +  2

  Slopes (m):  -1/2 (equal slopes)

  y- intercepts (b): 3 and 2

  System: Inconsistent

  Graph: parallel

  4) x + y = 1

  y = -x + 1

  2x - 3y = 8

  3y/3 = 2x/3 - 8/3

  y = 2x/3 - 8/3

  Slopes (m):  -1 and 2/3

  y- intercepts (b): 1 and -8/3

  System: Independent

  Graph: Intersects

  5) x + 3y = 6

  3y/3 = -x/3 + 6/3

  y = -x/3 + 2

  4x - y = 4

  y = 4x - 4

  Slopes (m):  -1/3 and 4

  y- intercepts (b): 2 and -4

  System: Independent

  Graph: Intersects

  6) 2x - y = 6

  y = 2x - 6

  -4x + 2y = 8

  2y/2 = 4x/2 + 8/2

  y = 2x + 4

  Slopes (m):  2 (equal slopes)

  y- intercepts (b): -6 and 4

  System: Inconsistent

  Graph: Parallel

  (Please click the image below and enlarge to view the graphs.)

  
  
• Réponse publiée par: meteor13

  a. falls to the left, rises to the right

  b.rises to the left, falls to the right

  c. falls to the left, rises to the right

  Step-by-step explanation:

  If the leading coefficient is positive ( greater than zero ), then the graph falls to the left and rises to the right. If the leading coefficient is negative ( less than zero ), then the graph rises to the left and falls to the right.
• Réponse publiée par: hajuyanadoy

  answer:

  hotdog 1 hotdog 2 hotdog 3