SOLUTION: Solve by elimination 0.05x+0.25y=66 0.15+0.05y=72

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Question 192048: Solve by elimination

0.05x+0.25y=66
0.15+0.05y=72



Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
0.05x%2B0.25y=66 Start with the first equation.


100%280.05x%2B0.25y%29=100%2866%29 Multiply both sides by 100 to clear out the decimals.


5x%2B25y=6600 Distribute and multiply.


0.15x%2B0.05y=72 Move onto the second equation.


100%280.15x%2B0.05y%29=100%2872%29 Multiply both sides by 100 to clear out the decimals.


15x%2B5y=7200 Distribute and multiply.


So we have the system of equations:


system%285x%2B25y=6600%2C15x%2B5y=7200%29


-5%2815x%2B5y%29=-5%287200%29 Multiply the both sides of the second equation by -5.


-75x-25y=-36000 Distribute and multiply.


So we have the new system of equations:
system%285x%2B25y=6600%2C-75x-25y=-36000%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=%286600%29%2B%28-36000%29


%285x%2B-75x%29%2B%2825y%2B-25y%29=6600%2B-36000 Group like terms.


-70x%2B0y=-29400 Combine like terms.


-70x=-29400 Simplify.


x=%28-29400%29%2F%28-70%29 Divide both sides by -70 to isolate x.


x=420 Reduce.


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5x%2B25y=6600 Now go back to the first equation.


5%28420%29%2B25y=6600 Plug in x=420.


2100%2B25y=6600 Multiply.


25y=6600-2100 Subtract 2100 from both sides.


25y=4500 Combine like terms on the right side.


y=%284500%29%2F%2825%29 Divide both sides by 25 to isolate y.


y=180 Reduce.


So the solutions are x=420 and y=180.


Which form the ordered pair .


This means that the system is consistent and independent.