SOLUTION: -4x+y=6 -5x-y+21

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Question 405162: -4x+y=6
-5x-y+21
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%2By=6%2C-5x-y=21%29


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%2By%29%2B%28-5x-y%29=%286%29%2B%2821%29


%28-4x-5x%29%2B%28y-y%29=6%2B21 Group like terms.


-9x%2B0y=27 Combine like terms. Notice how the y terms cancel out.


-9x=27 Simplify.


x=%2827%29%2F%28-9%29 Divide both sides by -9 to isolate x.


x=-3 Reduce.


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


-4x%2By=6 Now go back to the first equation.


-4%28-3%29%2By=6 Plug in x=-3.


12%2By=6 Multiply.


y=6-12 Subtract 12 from both sides.


y=-6 Combine like terms on the right side.


So our answer is x=-3 and y=-6.


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%2By=6 (red) and -5x-y=21 (green)


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