SOLUTION: 2x+4=4 y=-2x+4

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Question 201104: 2x+4=4
y=-2x+4
Found 2 solutions by jim_thompson5910, anahiperez:
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%2Cx%2B4y=5%29


-2%28x%2B4y%29=-2%285%29 Multiply the both sides of the second equation by -2.


-2x-8y=-10 Distribute and multiply.


So we have the new system of equations:
system%282x%2By=4%2C-2x-8y=-10%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:


%282x%2By%29%2B%28-2x-8y%29=%284%29%2B%28-10%29


%282x%2B-2x%29%2B%281y%2B-8y%29=4%2B-10 Group like terms.


0x%2B-7y=-6 Combine like terms.


-7y=-6 Simplify.


y=%28-6%29%2F%28-7%29 Divide both sides by -7 to isolate y.


y=6%2F7 Reduce.


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2x%2By=4 Now go back to the first equation.


2x%2B6%2F7=4 Plug in y=6%2F7.


7%282x%2B6%2Fcross%287%29%29=7%284%29 Multiply both sides by the LCD 7 to clear any fractions.


14x%2B6=28 Distribute and multiply.


14x=28-6 Subtract 6 from both sides.


14x=22 Combine like terms on the right side.


x=%2822%29%2F%2814%29 Divide both sides by 14 to isolate x.


x=11%2F7 Reduce.


So the solutions are x=11%2F7 and y=6%2F7.


Which form the ordered pair .


This means that the system is consistent and independent.


Answer by anahiperez(1) About Me  (Show Source):
You can put this solution on YOUR website!
2x+4=4
y=-2x+4