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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

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


    Practice exercises 4.1a. sketch the graph of the following linear systems. then tell whether the sys
    Practice exercises 4.1a. sketch the graph of the following linear systems. then tell whether the sys
    Practice exercises 4.1a. sketch the graph of the following linear systems. then tell whether the sys
    Practice exercises 4.1a. sketch the graph of the following linear systems. then tell whether the sys
    Practice exercises 4.1a. sketch the graph of the following linear systems. then tell whether the sys
  • 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.)


    Practice exercises 4.1a. sketch the graph of the following linear systems. then tell whether the sys
  • 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

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Practice exercises 4.1a. sketch the graph of the following linear systems. then tell whether the sys...