SOLUTION: What is the Solution to the system? 2x - 3y = -27 -3x + 2y = 23 [ I got -3 for my answer]

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Question 568396: What is the Solution to the system?


2x - 3y = -27
-3x + 2y = 23
[ I got -3 for my answer]
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=-27%2C-3x%2B2y=23%29


2%282x-3y%29=2%28-27%29 Multiply the both sides of the first equation by 2.


4x-6y=-54 Distribute and multiply.


3%28-3x%2B2y%29=3%2823%29 Multiply the both sides of the second equation by 3.


-9x%2B6y=69 Distribute and multiply.


So we have the new system of equations:
system%284x-6y=-54%2C-9x%2B6y=69%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:


%284x-6y%29%2B%28-9x%2B6y%29=%28-54%29%2B%2869%29


%284x%2B-9x%29%2B%28-6y%2B6y%29=-54%2B69 Group like terms.


-5x%2B0y=15 Combine like terms.


-5x=15 Simplify.


x=%2815%29%2F%28-5%29 Divide both sides by -5 to isolate x.


x=-3 Reduce.


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4x-6y=-54 Now go back to the first equation.


4%28-3%29-6y=-54 Plug in x=-3.


-12-6y=-54 Multiply.


-6y=-54%2B12 Add 12 to both sides.


-6y=-42 Combine like terms on the right side.


y=%28-42%29%2F%28-6%29 Divide both sides by -6 to isolate y.


y=7 Reduce.


So the solutions are x=-3 and y=7.


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=-27 (red) and -3x%2B2y=23 (green)


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