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

A. consistent.

B. inconsistent.

C. independent.

D. dependent.

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.

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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