SOLUTION: solve each system of linear equations by using addition or elimination 8) 2x - y = -4 4x + y = 1

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Question 241749: solve each system of linear equations by using addition or elimination
8) 2x - y = -4
4x + y = 1
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%282x-y=-4%2C4x%2By=1%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-y%29%2B%284x%2By%29=%28-4%29%2B%281%29


%282x%2B4x%29%2B%28-y%2By%29=-4%2B1 Group like terms.


6x%2B0y=-3 Combine like terms.


6x=-3 Simplify.


x=%28-3%29%2F%286%29 Divide both sides by 6 to isolate x.


x=-1%2F2 Reduce.


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2x-y=-4 Now go back to the first equation.


2%28-1%2F2%29-y=-4 Plug in x=-1%2F2.


-1-y=-4 Multiply.


-y=-4%2B1 Add 1 to both sides.


-y=-3 Combine like terms on the right side.


y=%28-3%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=3 Reduce.


So the solutions are x=-1%2F2 and y=3.


Which form the ordered pair .


This means that the system is consistent and independent.