SOLUTION: Please help with question slove using the elemination method x+5y=-6 2x+5y=3

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Question 281923: Please help with question
slove using the elemination method
x+5y=-6
2x+5y=3
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%28x%2B5y=-6%2C2x%2B5y=3%29


-1%28x%2B5y%29=-1%28-6%29 Multiply the both sides of the first equation by -1.


-x-5y=6 Distribute and multiply.


So we have the new system of equations:
system%28-x-5y=6%2C2x%2B5y=3%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-x-5y%29%2B%282x%2B5y%29=%286%29%2B%283%29


%28-x%2B2x%29%2B%28-5y%2B5y%29=6%2B3 Group like terms.


x%2B0y=9 Combine like terms.


x=9 Simplify.


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


-x-5y=6 Now go back to the first equation.


-9-5y=6 Plug in x=9.


-9-5y=6 Multiply.


-5y=6%2B9 Add 9 to both sides.


-5y=15 Combine like terms on the right side.


y=%2815%29%2F%28-5%29 Divide both sides by -5 to isolate y.


y=-3 Reduce.


So the solutions are x=9 and y=-3.


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 x%2B5y=-6 (red) and 2x%2B5y=3 (green)