SOLUTION: Solve the given system by use of elimination: 0.3x-0.2y=4 0.5x+0.3y=1

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Question 202422: Solve the given system by use of elimination:

0.3x-0.2y=4
0.5x+0.3y=1



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.


10%280.3x%29-10%280.2y%29=10%284%29 Multiply EVERY term by 10 to make every number a whole number.


3x-2y=40 Multiply

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0.5x%2B0.3y=1 Move onto the second equation.


10%280.5x%29%2B10%280.3y%29=10%281%29 Multiply EVERY term by 10 to make every number a whole number.


5x%2B3y=10 Multiply



So we have the given system of equations:

system%283x-2y=40%2C5x%2B3y=10%29


3%283x-2y%29=3%2840%29 Multiply the both sides of the first equation by 3.


9x-6y=120 Distribute and multiply.


2%285x%2B3y%29=2%2810%29 Multiply the both sides of the second equation by 2.


10x%2B6y=20 Distribute and multiply.


So we have the new system of equations:

system%289x-6y=120%2C10x%2B6y=20%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:


%289x-6y%29%2B%2810x%2B6y%29=%28120%29%2B%2820%29


%289x%2B10x%29%2B%28-6y%2B6y%29=120%2B20 Group like terms.


19x%2B0y=140 Combine like terms.


19x=140 Simplify.


x=%28140%29%2F%2819%29 Divide both sides by 19 to isolate x.


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9x-6y=120 Now go back to the first equation.


9%28140%2F19%29-6y=120 Plug in x=140%2F19.


1260%2F19-6y=120 Multiply.


cross%2819%29%281260%2Fcross%2819%29%29-19%286y%29=19%28120%29 Multiply both sides by the LCD 19 to clear any fractions.


1260-114y=2280 Distribute and multiply.


-114y=2280-1260 Subtract 1260 from both sides.


-114y=1020 Combine like terms on the right side.


y=%281020%29%2F%28-114%29 Divide both sides by -114 to isolate y.


y=-170%2F19 Reduce.


So the solutions are x=140%2F19 and y=-170%2F19.


Which form the ordered pair .


This means that the system is consistent and independent.


Note: the approximate solutions are x=7.368 and y=-8.947