SOLUTION: Solve by using elimination method. -4x-2y=3 2x+y=1 separate problem: 2x+y=1 -x-y=-3

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Question 244763: Solve by using elimination method.
-4x-2y=3
2x+y=1

separate problem:
2x+y=1
-x-y=-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

Start with the given system of equations:
system%28-4x-2y=3%2C2x%2By=1%29


2%282x%2By%29=2%281%29 Multiply the both sides of the second equation by 2.


4x%2B2y=2 Distribute and multiply.


So we have the new system of equations:
system%28-4x-2y=3%2C4x%2B2y=2%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28-4x-2y%29%2B%284x%2B2y%29=%283%29%2B%282%29


%28-4x%2B4x%29%2B%28-2y%2B2y%29=3%2B2 Group like terms.


0x%2B0y=5 Combine like terms.


0=5Simplify.


Since 0=5 is NEVER true, this means that there are no solutions.


So the system is inconsistent.



# 2


Start with the given system of equations:
system%282x%2By=1%2C-x-y=-3%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%282x%2By%29%2B%28-x-y%29=%281%29%2B%28-3%29


%282x-x%29%2B%28y-y%29=1-3 Group like terms.


x%2B0y=-2 Combine like terms.


x=-2 Simplify.


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


2x%2By=1 Now go back to the first equation.


2%28-2%29%2By=1 Plug in x=-2.


-4%2By=1 Multiply.


y=1%2B4 Add 4 to both sides.


y=5 Combine like terms on the right side.


So the solutions are x=-2 and y=5.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 2x%2By=1 (red) and -x-y=-3 (green)