SOLUTION: Please Help. Use elimination to solve each system of equations. 2X-3Y=9 -5X-3Y=30

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Question 182609: Please Help.
Use elimination to solve each system of equations.
2X-3Y=9 -5X-3Y=30
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%282x-3y=9%2C-5x-3y=30%29


-1%28-5x-3y%29=-1%2830%29 Multiply the both sides of the second equation by -1.


5x%2B3y=-30 Distribute and multiply.


So we have the new system of equations:
system%282x-3y=9%2C5x%2B3y=-30%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:


%282x-3y%29%2B%285x%2B3y%29=%289%29%2B%28-30%29


%282x%2B5x%29%2B%28-3y%2B3y%29=9%2B-30 Group like terms.


7x%2B0y=-21 Combine like terms.


7x=-21 Simplify.


x=%28-21%29%2F%287%29 Divide both sides by 7 to isolate x.


x=-3 Reduce.


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2x-3y=9 Now go back to the first equation.


2%28-3%29-3y=9 Plug in x=-3.


-6-3y=9 Multiply.


-3y=9%2B6 Add 6 to both sides.


-3y=15 Combine like terms on the right side.


y=%2815%29%2F%28-3%29 Divide both sides by -3 to isolate y.


y=-5 Reduce.


So our answer is x=-3 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 2x-3y=9 (red) and -5x-3y=30 (green)