SOLUTION: Solve by elimination method: -2x+2y=-1 x-3y=-3

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Question 677171: Solve by elimination method:
-2x+2y=-1
x-3y=-3
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%28-2x%2B2y=-1%2Cx-3y=-3%29


2%28x-3y%29=2%28-3%29 Multiply the both sides of the second equation by 2.


2x-6y=-6 Distribute and multiply.


So we have the new system of equations:
system%28-2x%2B2y=-1%2C2x-6y=-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%2B2y%29%2B%282x-6y%29=%28-1%29%2B%28-6%29


%28-2x%2B2x%29%2B%282y%2B-6y%29=-1%2B-6 Group like terms.


0x%2B-4y=-7 Combine like terms.


-4y=-7 Simplify.


y=%28-7%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=7%2F4 Reduce.


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


-2x%2B2%287%2F4%29=-1 Plug in y=7%2F4.


-2x%2B7%2F2=-1 Multiply.


2%28-2x%2B7%2Fcross%282%29%29=2%28-1%29 Multiply both sides by the LCD 2 to clear any fractions.


-4x%2B7=-2 Distribute and multiply.


-4x=-2-7 Subtract 7 from both sides.


-4x=-9 Combine like terms on the right side.


x=%28-9%29%2F%28-4%29 Divide both sides by -4 to isolate x.


x=9%2F4 Reduce.


So the solutions are x=9%2F4 and y=7%2F4.


Which form the ordered pair .


This means that the system is consistent and independent.