SOLUTION: can you please help me solve this: Solve by the elimination method 9x-y=33 x+3y=13

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Question 683912: can you please help me solve this:
Solve by the elimination method
9x-y=33
x+3y=13
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%289x-y=33%2Cx%2B3y=13%29


3%289x-y%29=3%2833%29 Multiply the both sides of the first equation by 3.


27x-3y=99 Distribute and multiply.


So we have the new system of equations:
system%2827x-3y=99%2Cx%2B3y=13%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:


%2827x-3y%29%2B%28x%2B3y%29=%2899%29%2B%2813%29


%2827x%2B1x%29%2B%28-3y%2B3y%29=99%2B13 Group like terms.


28x%2B0y=112 Combine like terms.


28x=112 Simplify.


x=%28112%29%2F%2828%29 Divide both sides by 28 to isolate x.


x=4 Reduce.


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27x-3y=99 Now go back to the first equation.


27%284%29-3y=99 Plug in x=4.


108-3y=99 Multiply.


-3y=99-108 Subtract 108 from both sides.


-3y=-9 Combine like terms on the right side.


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


y=3 Reduce.


So the solutions are x=4 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 9x-y=33 (red) and x%2B3y=13 (green)