SOLUTION: -4x+9y=9 x-3y=-6 how do this problem by elimination?

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Question 264568: -4x+9y=9
x-3y=-6
how do this problem by elimination?
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%2B9y=9%2Cx-3y=-6%29


3%28x-3y%29=3%28-6%29 Multiply the both sides of the second equation by 3.


3x-9y=-18 Distribute and multiply.


So we have the new system of equations:
system%28-4x%2B9y=9%2C3x-9y=-18%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:


%28-4x%2B9y%29%2B%283x-9y%29=%289%29%2B%28-18%29


%28-4x%2B3x%29%2B%289y%2B-9y%29=9%2B-18 Group like terms.


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


-x=-9 Simplify.


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


x=9 Reduce.


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-4x%2B9y=9 Now go back to the first equation.


-4%289%29%2B9y=9 Plug in x=9.


-36%2B9y=9 Multiply.


9y=9%2B36 Add 36 to both sides.


9y=45 Combine like terms on the right side.


y=%2845%29%2F%289%29 Divide both sides by 9 to isolate y.


y=5 Reduce.


So the solutions are x=9 and y=5.


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%2B9y=9 (red) and x-3y=-6 (green)