SOLUTION: 10x+15y=20 -9x-15y=-21

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Question 549803: 10x+15y=20
-9x-15y=-21
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%2810x%2B15y=20%2C-9x-15y=-21%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%2810x%2B15y%29%2B%28-9x-15y%29=%2820%29%2B%28-21%29


%2810x%2B-9x%29%2B%2815y%2B-15y%29=20%2B-21 Group like terms.


x%2B0y=-1 Combine like terms.


x=-1 Simplify.


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10x%2B15y=20 Now go back to the first equation.


10%28-1%29%2B15y=20 Plug in x=-1.


-10%2B15y=20 Multiply.


15y=20%2B10 Add 10 to both sides.


15y=30 Combine like terms on the right side.


y=%2830%29%2F%2815%29 Divide both sides by 15 to isolate y.


y=2 Reduce.


So the solutions are x=-1 and y=2.


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 10x%2B15y=20 (red) and -9x-15y=-21 (green)