SOLUTION: Solve the system by addition: x-y = -1 5x+2y = 30

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Question 376337: Solve the system by addition:
x-y = -1
5x+2y = 30
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 first equation by 2.


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.


Simplify.


Divide both sides by to isolate .


Reduce.


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


Now go back to the first equation.


Plug in .


Multiply.


Subtract from both sides.


Combine like terms on the right side.


Divide both sides by to isolate .


Reduce.


So the solutions are 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)


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim
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