SOLUTION: How many solutions are in the equation: (-2x+y=1, -4x+2y=-8)

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Question 152569: How many solutions are in the equation: (-2x+y=1, -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%28-2x%2By=1%2C-4x%2B2y=-8%29


-2%28-2x%2By%29=-2%281%29 Multiply the both sides of the first equation by -2.


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


So we have the new system of equations:
system%284x-2y=-2%2C-4x%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:


%284x-2y%29%2B%28-4x%2B2y%29=%28-2%29%2B%28-8%29


%284x%2B-4x%29%2B%28-2y%2B2y%29=-2%2B-8 Group like terms.


0x%2B0y=-10 Combine like terms. Notice how the x terms cancel out.


0=-10Simplify.


Since 0=-10 is never true, this means that there are no solutions. So the system is inconsistent.