SOLUTION: Solve the system by substitution: -3x+6y=21 2x-4y=14 I have tryed completing this by making the -3x+6y=21 into an x=2y-7. Then I got 2(2y-7)-4y=14 which turns into 4y-14-4y=1

Question 469016: Solve the system by substitution:
-3x+6y=21
2x-4y=14
I have tryed completing this by making the -3x+6y=21 into an x=2y-7.
Then I got 2(2y-7)-4y=14 which turns into 4y-14-4y=14 and then -14=14.
If this problem is not possible, then what do I write as an answer??
Thank you so so so so so so much! (:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Add to both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

---------------------

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Multiply both sides by the LCM of 2. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)

Distribute and multiply the LCM to each side

Combine like terms on the left side

Add 28 to both sides

Combine like terms on the right side

Since this equation is NEVER true for any x value, this means there are no solutions.

So consequently, there are no solutions for the system of equations.

So the system is inconsistent.

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