SOLUTION: -9=x-3y -2x+6=6y

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Question 147493: -9=x-3y
-2x+6=6y
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-9=x-3y Start with the first equation.


0=x-3y%2B9 Add 9 to both sides.


-x=-3y%2B9 Subtract x from both sides.


-x%2B3y=9 Add 3y to both sides.


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-2x%2B6=6y Start with the second equation.


-2x=6y-6 Subtract 6 from both sides.


-2x-6y=-6 Subtract 6y from both sides.


So we have the system of equations:


system%28-x%2B3y=9%2C-2x-6y=-6%29


2%28-x%2B3y%29=2%289%29 Multiply the both sides of the first equation by 2.


-2x%2B6y=18 Distribute and multiply.


-1%28-2x-6y%29=-1%28-6%29 Multiply the both sides of the second equation by -1.


2x%2B6y=6 Distribute and multiply.


So we have the new system of equations:
system%28-2x%2B6y=18%2C2x%2B6y=6%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:


%28-2x%2B6y%29%2B%282x%2B6y%29=%2818%29%2B%286%29


%28-2x%2B2x%29%2B%286y%2B6y%29=18%2B6 Group like terms.


0x%2B12y=24 Combine like terms. Notice how the x terms cancel out.


12y=24 Simplify.


y=%2824%29%2F%2812%29 Divide both sides by 12 to isolate y.


y=2 Reduce.


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-2x%2B6y=18 Now go back to the first equation.


-2x%2B6%282%29=18 Plug in y=2.


-2x%2B12=18 Multiply.


-2x=18-12 Subtract 12 from both sides.


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


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


x=-3 Reduce.


So our answer is x=-3 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 -x%2B3y=9 (red) and -2x-6y=-6 (green)