SOLUTION: Solve the given system by use of elimination: 0.05x+0.25y=11 0.15x+0.05y=12

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Question 202425: Solve the given system by use of elimination:

0.05x+0.25y=11
0.15x+0.05y=12





Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
0.05x%2B0.25y=11 Start with the first equation.


100%280.05x%29%2B100%280.25y%29=100%2811%29 Multiply EVERY term by 100 to make every value a whole number.


5x%2B25y=1100 Multiply.

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0.15x%2B0.05y=12 Move onto the second equation.


100%280.15x%29%2B100%280.05y%29=100%2812%29 Multiply EVERY term by 100 to make every value a whole number.


15x%2B5y=1200 Multiply.



So we have the given system of equations:

system%285x%2B25y=1100%2C15x%2B5y=1200%29


-5%2815x%2B5y%29=-5%281200%29 Multiply the both sides of the second equation by -5.


-75x-25y=-6000 Distribute and multiply.


So we have the new system of equations:

system%285x%2B25y=1100%2C-75x-25y=-6000%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:


%285x%2B25y%29%2B%28-75x-25y%29=%281100%29%2B%28-6000%29


%285x-75x%29%2B%2825y-25y%29=1100%2B-6000 Group like terms.


-70x%2B0y=-4900 Combine like terms.


-70x=-4900 Simplify.


x=%28-4900%29%2F%28-70%29 Divide both sides by -70 to isolate x.


x=70 Reduce.


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5x%2B25y=1100 Now go back to the first equation.


5%2870%29%2B25y=1100 Plug in x=70.


350%2B25y=1100 Multiply.


25y=1100-350 Subtract 350 from both sides.


25y=750 Combine like terms on the right side.


y=%28750%29%2F%2825%29 Divide both sides by 25 to isolate y.


y=30 Reduce.


So the solutions are x=70 and y=30.


Which form the ordered pair .


This means that the system is consistent and independent.