SOLUTION: Use linear combinations to solve the system of linear equations. x+3y=12 -3y+x=30

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Question 176233: Use linear combinations to solve the system of linear equations.
x+3y=12
-3y+x=30
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%28x%2B3y=12%2Cx-3y=30%29

Note: I've rearrange the terms in the second equation


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


%28x%2B3y%29%2B%28x-3y%29=%2812%29%2B%2830%29


%28x%2Bx%29%2B%283y-3y%29=12%2B30 Group like terms.


2x%2B0y=42 Combine like terms.


2x=42 Simplify.


x=%2842%29%2F%282%29 Divide both sides by 2 to isolate x.


x=21 Reduce.


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


x%2B3y=12 Now go back to the first equation.


21%2B3y=12 Plug in x=21.


21%2B3y=12 Multiply.


3y=12-21 Subtract 21 from both sides.


3y=-9 Combine like terms on the right side.


y=%28-9%29%2F%283%29 Divide both sides by 3 to isolate y.


y=-3 Reduce.


So our answer is x=21 and y=-3.


Which form the ordered pair .


This means that the system is consistent and independent.