Question

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

A. consistent.
B. inconsistent.
C. independent.
D. dependent.

Answer 1

The system is inconsistent because there is no solution.

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.

Answer 2

B) Inconsistent

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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