Is the equations 3x-6y equals 20 and 2x-4y equals 3 consistent or inconsistent?

Answer 1

3x-6y=20

2x-4y=3

Is suggest you use elimination to solve this problem because it's easier. Eliminate either your Xs or your Ys.

(2)(3x-6y)=40

-3(2x-4y)=-9 (note that you multiplied by a -3, not a +3, because you are trying to get opposites.

6x-12y=40

-6x+12y=-9

You can eliminate your 6x and -6x because they are opposites.

0y=31

Divide by 0 on each side.

y=0

Now plug in what y equals or 0 into one of the original equations to find the value of x.

3x-6y=20

3x-6(0)=20

3x-0=20

Add 0 to both sides.

3x=20

Divide by 3 on each side.

x=6.6666666666666666666666

To check your work, plug in 6.6666666666666666666 for x and 0 for y in one of the original equations. If you come up with a true statement, then you know you have the correct values for x and y.

3x-6y=20

3(6.6666666666666666666666)-6(0)=20

20-0=20

20=20

Because this is a true statement, you can be sure that you have the correct values for x and y.

3x-6y=20

2x-4y=3

Now get y by itself to find out if the equations are consistent or inconsistent.

Subtract 3x on both sides.

-6y=20-3x

Divide by -6 on each side

y=-3.33333333333333333333333+1/2x

Subtract 2x on both sides.

-4y=3-2x

Divide by -4 on each side.

y=-3/4+1/2x

These equations are consistent because they have the same slopes.