SOLUTION: i want to ask help from you to please help me solve this system by comparison? -2x+3y=15,-6x+6y=18

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Question 325300: i want to ask help from you to please help me solve this system by comparison?
-2x+3y=15,-6x+6y=18
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not familiar with the "comparison" method, but here's how to do it via the elimination method.



Start with the given system of equations:
system%28-2x%2B3y=15%2C-6x%2B6y=18%29


-2%28-2x%2B3y%29=-2%2815%29 Multiply the both sides of the first equation by -2.


4x-6y=-30 Distribute and multiply.


So we have the new system of equations:
system%284x-6y=-30%2C-6x%2B6y=18%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%28-6x%2B6y%29=%28-30%29%2B%2818%29


%284x-6x%29%2B%28-6y%2B6y%29=-30%2B18 Group like terms.


-2x%2B0y=-12 Combine like terms.


-2x=-12 Simplify.


x=%28-12%29%2F%28-2%29 Divide both sides by -2 to isolate x.


x=6 Reduce.


------------------------------------------------------------------


4x-6y=-30 Now go back to the first equation.


4%286%29-6y=-30 Plug in x=6.


24-6y=-30 Multiply.


-6y=-30-24 Subtract 24 from both sides.


-6y=-54 Combine like terms on the right side.


y=%28-54%29%2F%28-6%29 Divide both sides by -6 to isolate y.


y=9 Reduce.


So the solutions are x=6 and y=9.


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%2B3y=15 (red) and -6x%2B6y=18 (green)