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24 August, 13:34

The system of equations 3x - 6y = 20 and 2x - 4y = 3 is

A. consistent.

B. inconsistent.

C. independent.

D. dependent.

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Answers (2)
  1. 24 August, 16:01
    0
    The system is inconsistent because there is no solution.

    Step-by-step explanation:

    I'm going to put both of these in slope-intercept form (y=mx+b where m is slope and b is y-intercept).

    3x-6y=20

    Solve for y.

    3x-6y=20

    Subtract 3x on both sides:

    -6y=-3x+20

    Divide both sides by - 6:

    y = (-3/-6) x + (20/-6)

    Reduce:

    y = (1/2) x + (-10/3)

    The slope is 1/2 and the y-intercept is - 10/3.

    2x-4y=3

    Solve for y.

    2x-4y=3

    Subtract 2x on both sides:

    -4y=-2x+3

    Divide both sides by - 4:

    y = (-2/-4) x + (3/-4)

    Reduce:

    y = (1/2) x + (-3/4)

    The slope is 1/2 and the y-intercept is - 3/4.

    The lines are parallel so they have no intersection. I know they are parallel because they have the same slope and different y-intercept.

    The system is inconsistent because there is no solution.
  2. 24 August, 16:18
    0
    B) Inconsistent

    Step-by-step explanation:

    Step 1: Write both equations

    3x - 6y = 20

    2x - 4y = 3

    Step 2: Find x in terms of y

    3x - 6y = 20

    x = 20+6y/3

    Step 3: Substitute x in one of the equations to find y

    2x - 4y = 3

    2 (20+6y/3) - 5y = 3

    40 + 12y - 12y = 9

    0 ≠ - 31

    Therefore, these system of equations have no solution.

    Step 4: Choose the option

    A) consistent - A consistent system of equations has at least one set of equations. Therefore, this option is incorrect.

    B) inconsistent - An inconsistent system of equations has no solution. Therefore, this option is correct.

    C) Independent - An independent system of equations has one solution. Therefore, this option is incorrect.

    D) Dependent - A dependent system of equations have infinite solutions. Therefore, this option is incorrect.

    Option B is the right answer

    !
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