SOLUTION: Solve by the elimination method. 0.3x-0.2y=4 0.2x+0.3y=5/23

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Question 193227: Solve by the elimination method.
0.3x-0.2y=4
0.2x+0.3y=5/23


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
0.3x-0.2y=4 Start with the first equation.


3x-2y=40 Multiply EVERY term by 10 to make every number a whole number.

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0.2x%2B0.3y=5%2F23 Move onto the second equation.


23%280.2x%29%2B23%280.3y%29=cross%2823%29%285%2Fcross%2823%29%29 Multiply EVERY term by the LCD 23 to clear out the fraction.


4.6x%2B6.9y=5 Multiply and simplify


46x%2B69y=50 Multiply EVERY term by 10 to make every number a whole number.


So we have the system of equations:

system%283x-2y=40%2C46x%2B69y=50%29


69%283x-2y%29=69%2840%29 Multiply the both sides of the first equation by 69.


207x-138y=2760 Distribute and multiply.


2%2846x%2B69y%29=2%2850%29 Multiply the both sides of the second equation by 2.


92x%2B138y=100 Distribute and multiply.


So we have the new system of equations:

system%28207x-138y=2760%2C92x%2B138y=100%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:


%28207x-138y%29%2B%2892x%2B138y%29=%282760%29%2B%28100%29


%28207x%2B92x%29%2B%28-138y%2B138y%29=2760%2B100 Group like terms.


299x%2B0y=2860 Combine like terms.


299x=2860 Simplify.


x=%282860%29%2F%28299%29 Divide both sides by 299 to isolate x.


x=220%2F23 Reduce.


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207x-138y=2760 Now go back to the first equation.


207%28220%2F23%29-138y=2760 Plug in x=220%2F23.


1980-138y=2760 Multiply.


-138y=2760-1980 Subtract 1980 from both sides.


-138y=780 Combine like terms on the right side.


y=%28780%29%2F%28-138%29 Divide both sides by -138 to isolate y.


y=-130%2F23 Reduce.

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Answer:


So the solutions are x=220%2F23 and y=-130%2F23


which form the ordered pair