SOLUTION: 3x-2y=0 and x+y=-5 what is x and y equal too?

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Question 176474This question is from textbook
: 3x-2y=0 and x+y=-5 what is x and y equal too? This question is from textbook

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%283x-2y=0%2Cx%2By=-5%29


2%28x%2By%29=2%28-5%29 Multiply the both sides of the second equation by 2.


2x%2B2y=-10 Distribute and multiply.


So we have the new system of equations:
system%283x-2y=0%2C2x%2B2y=-10%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:


%283x-2y%29%2B%282x%2B2y%29=%280%29%2B%28-10%29


%283x%2B2x%29%2B%28-2y%2B2y%29=0%2B-10 Group like terms.


5x%2B0y=-10 Combine like terms.


5x=-10 Simplify.


x=%28-10%29%2F%285%29 Divide both sides by 5 to isolate x.


x=-2 Reduce.


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3x-2y=0 Now go back to the first equation.


3%28-2%29-2y=0 Plug in x=-2.


-6-2y=0 Multiply.


-2y=0%2B6 Add 6 to both sides.


-2y=6 Combine like terms on the right side.


y=%286%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=-3 Reduce.


So our answer is x=-2 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 3x-2y=0 (red) and x%2By=-5 (green)