SOLUTION: y=2x-5 and y+1=2(x-2)addition method and is it independent, dependent or inconsistent. x+y=4 and x-y=5 addition method is it independent, dependent or inconsistent.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: y=2x-5 and y+1=2(x-2)addition method and is it independent, dependent or inconsistent. x+y=4 and x-y=5 addition method is it independent, dependent or inconsistent.       Log On


   

Question 319716: y=2x-5 and y+1=2(x-2)addition method and is it independent, dependent or inconsistent.
x+y=4 and x-y=5 addition method is it independent, dependent or inconsistent.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the second one and let you do the first.

# 2



Start with the given system of equations:
system%28x%2By=4%2Cx-y=5%29


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


%28x%2By%29%2B%28x-1y%29=%284%29%2B%285%29


%281x%2B1x%29%2B%281y%2B-1y%29=4%2B5 Group like terms.


2x%2B0y=9 Combine like terms.


2x=9 Simplify.


x=%289%29%2F%282%29 Divide both sides by 2 to isolate x.


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


9%2F2%2By=4 Plug in x=9%2F2.


2%289%2Fcross%282%29%2By%29=2%284%29 Multiply both sides by the LCD 2 to clear any fractions.


9%2B2y=8 Distribute and multiply.


2y=8-9 Subtract 9 from both sides.


2y=-1 Combine like terms on the right side.


y=%28-1%29%2F%282%29 Divide both sides by 2 to isolate y.


So the solutions are x=9%2F2 and y=-1%2F2.


Which form the ordered pair .


This means that the system is consistent and independent.


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
y=2x-5 and y+1=2(x-2)addition method and is it independent, dependent or inconsistent.
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y=2x-5 and y+1=2(x-2)
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Rearrange the two equations:
y - 2x = -5
y - 2x = -5
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They are the same so they are dependent.
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x+y=4 and x-y=5 addition method is it independent, dependent or inconsistent.
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x+y = 4
x-y = 5
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Add to get:
2x = 9
x = 9/2
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Since x+y = 4, y = -1/2
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With a single solution they are independent.
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Cheers,
Stan H.
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