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)   (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:



Multiply the both sides of the second equation by -1.


Distribute and multiply.


So we have the new system of equations:



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





Group like terms.


Combine like terms. Notice how the y terms cancel out.


Simplify.


Divide both sides by to isolate .


Reduce.


------------------------------------------------------------------


Now go back to the first equation.


Plug in .


Multiply.


Remove any zero terms.


Divide both sides by to isolate .


Reduce.


So our answer is and .


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 (red) and (green)

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

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