SOLUTION: give the corrdinates of intersection of the linear equations 2x+y= -4 4x+2y=-8

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Question 218279: give the corrdinates of intersection of the linear equations
2x+y= -4
4x+2y=-8
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%2By=-4%2C4x%2B2y=-8%29


-2%282x%2By%29=-2%28-4%29 Multiply the both sides of the first equation by -2.


-4x-2y=8 Distribute and multiply.


So we have the new system of equations:
system%28-4x-2y=8%2C4x%2B2y=-8%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=%288%29%2B%28-8%29


%28-4x%2B4x%29%2B%28-2y%2B2y%29=8%2B-8 Group like terms.


0x%2B0y=0 Combine like terms. Notice how the x terms cancel out.


0=0Simplify.


Since 0=0 is always true, this means that there are an infinite number of solutions.


So the system is consistent and dependent.


Visually, this means that one graph is right on top of the other.