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

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

system%28-3x%2B6y=21%2C2x-4y=14%29



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

-3x%2B6y=21 Start with the first equation


6y=21%2B3x Add 3x to both sides


6y=%2B3x%2B21 Rearrange the equation


y=%28%2B3x%2B21%29%2F%286%29 Divide both sides by 6


y=%28%28%2B3%29%2F%286%29%29x%2B%2821%29%2F%286%29 Break up the fraction


y=%281%2F2%29x%2B7%2F2 Reduce



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

Since y=%281%2F2%29x%2B7%2F2, we can now replace each y in the second equation with %281%2F2%29x%2B7%2F2 to solve for x



2x-4highlight%28%28%281%2F2%29x%2B7%2F2%29%29=14 Plug in y=%281%2F2%29x%2B7%2F2 into the second equation. In other words, replace each y with %281%2F2%29x%2B7%2F2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



2x%2B%28-4%29%281%2F2%29x%2B%28-4%29%287%2F2%29=14 Distribute -4 to %281%2F2%29x%2B7%2F2


2x-%284%2F2%29x-28%2F2=14 Multiply


%282%29%282x-%284%2F2%29x-28%2F2%29=%282%29%2814%29 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)



4x-4x-28=28 Distribute and multiply the LCM to each side



-28=28 Combine like terms on the left side


0=28%2B28Add 28 to both sides


0=56 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.