SOLUTION: -x+2y=16 x-3y=-21

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Question 236841: -x+2y=16
x-3y=-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%28-x%2B2y=16%2Cx-3y=-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:


%28-1x%2B2y%29%2B%28x-3y%29=%2816%29%2B%28-21%29


%28-1x%2B1x%29%2B%282y%2B-3y%29=16%2B-21 Group like terms.


0x%2B-y=-5 Combine like terms. Notice how the x terms cancel out.


-y=-5 Simplify.


y=%28-5%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=5 Reduce.


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-1x%2B2y=16 Now go back to the first equation.


-1x%2B2%285%29=16 Plug in y=5.


-1x%2B10=16 Multiply.


-x=16-10 Subtract 10 from both sides.


-x=6 Combine like terms on the right side.


x=%286%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=-6 Reduce.


So our answer is x=-6 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 -x%2B2y=16 (red) and x-3y=-21 (green)