SOLUTION: How do you begin to solve -4x+2y=10 over 6x+2y=10

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Question 154283: How do you begin to solve -4x+2y=10 over 6x+2y=10
Found 2 solutions by jim_thompson5910, stanbon:
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%28-4x%2B2y=10%2C6x%2B2y=10%29


-1%286x%2B2y%29=-1%2810%29 Multiply the both sides of the second equation by -1.


-6x-2y=-10 Distribute and multiply.


So we have the new system of equations:
system%28-4x%2B2y=10%2C-6x-2y=-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:


%28-4x%2B2y%29%2B%28-6x-2y%29=%2810%29%2B%28-10%29


%28-4x%2B-6x%29%2B%282y%2B-2y%29=10%2B-10 Group like terms.


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


-10x=0 Simplify.


x=%280%29%2F%28-10%29 Divide both sides by -10 to isolate x.


x=0 Reduce.


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-4x%2B2y=10 Now go back to the first equation.


-4%280%29%2B2y=10 Plug in x=0.


0%2B2y=10 Multiply.


2y=10 Remove any zero terms.


y=%2810%29%2F%282%29 Divide both sides by 2 to isolate y.


y=5 Reduce.


So our answer is x=0 and y=5.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of -4x%2B2y=10 (red) and 6x%2B2y=10 (green)

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
-4x+2y=10
6x+2y=10
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Subtract the 1st equation from the 2nd to get:
10x = 0
x = 0
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Substitute into 6x+2y = 10 to solve for "y":
6*0 + 2y = 10
y = 5
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cheers,
Stan H.