SOLUTION: -x+3y=0 2x+6y+12

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Question 201631: -x+3y=0
2x+6y+12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that the second "equation" should be 2x%2B6y=12. You need to be more careful...



Start with the given system of equations:
system%28-x%2B3y=0%2C2x%2B6y=12%29


2%28-x%2B3y%29=2%280%29 Multiply the both sides of the first equation by 2.


-2x%2B6y=0 Distribute and multiply.


So we have the new system of equations:
system%28-2x%2B6y=0%2C2x%2B6y=12%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=%280%29%2B%2812%29


%28-2x%2B2x%29%2B%286y%2B6y%29=0%2B12 Group like terms.


0x%2B12y=12 Combine like terms.


12y=12 Simplify.


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


y=1 Reduce.


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-2x%2B6y=0 Now go back to the first equation.


-2x%2B6%281%29=0 Plug in y=1.


-2x%2B6=0 Multiply.


-2x=0-6 Subtract 6 from both sides.


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


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


x=3 Reduce.


So the solutions are x=3 and y=1.


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=0 (red) and 2x%2B6y=12 (green)