SOLUTION: 4x-2y=-6 2x-y=-3

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Question 178512: 4x-2y=-6
2x-y=-3
Found 2 solutions by jim_thompson5910, Alan3354:
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%284x-2y=-6%2C2x-y=-3%29


-2%282x-y%29=-2%28-3%29 Multiply the both sides of the second equation by -2.


-4x%2B2y=6 Distribute and multiply.


So we have the new system of equations:
system%284x-2y=-6%2C-4x%2B2y=6%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=%28-6%29%2B%286%29


%284x%2B-4x%29%2B%28-2y%2B2y%29=-6%2B6 Group like terms.


0x%2B0y=0 Combine like terms.


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.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
4x-2y=-6
2x-y=-3
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You didn't say what you want to do, but...
The 1st eqn is 2 times the first, so no unique solution is possible.
If you graph it, it's a straight line of infinite length, and all points on it satisfy the equation.