Questions on Algebra: Systems of Linear Equations answered by real tutors!

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Question 152569: How many solutions are in the equation: (-2x+y=1, -4x+2y=-8): How many solutions are in the equation: (-2x+y=1, -4x+2y=-8)
Answer by jim_thompson5910(9368) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system(-2x+y=1,-4x+2y=-8)


-2(-2x+y)=-2(1) 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(4x-2y=-2,-4x+2y=-8)


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


(4x-2y)+(-4x+2y)=(-2)+(-8)


(4x+-4x)+(-2y+2y)=-2+-8 Group like terms.


0x+0y=-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.