SOLUTION: using the elimination method if the system has no solution or an infinite number of solutions -7x- y = -30 4x + y = 21

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Question 590778: using the elimination method if the system has no solution or an infinite number of solutions
-7x- y = -30
4x + 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%28-7x-y=-30%2C4x%2By=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:


%28-7x-y%29%2B%284x%2By%29=%28-30%29%2B%2821%29


%28-7x%2B4x%29%2B%28-y%2By%29=-30%2B21 Group like terms.


-3x%2B0y=-9 Combine like terms.


-3x=-9 Simplify.


x=%28-9%29%2F%28-3%29 Divide both sides by -3 to isolate x.


x=3 Reduce.


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-7x-y=-30 Now go back to the first equation.


-7%283%29-y=-30 Plug in x=3.


-21-y=-30 Multiply.


-y=-30%2B21 Add 21 to both sides.


-y=-9 Combine like terms on the right side.


y=%28-9%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=9 Reduce.


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


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 -7x-y=-30 (red) and 4x%2By=21 (green)


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