SOLUTION: Solve by elimination 0.3x-0.2y=4 0.5x+0.3y=-7/17

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve by elimination 0.3x-0.2y=4 0.5x+0.3y=-7/17       Log On


   

Question 192046: Solve by elimination

0.3x-0.2y=4
0.5x+0.3y=-7/17


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


0.5x%2B0.3y=-7%2F17 Move onto the second equation


17%280.5x%29%2B17%280.3y%29=cross%2817%29%28-7%2Fcross%2817%29%29 Multiply EVERY term by the LCD 17 to clear out the fractions.


8.5x%2B5.1y=-7 Multiply


85x%2B51y=-70 Multiply EVERY term by 10 to make every number a whole number


So we have the system of equations:

system%283x-2y=40%2C85x%2B51y=-70%29


51%283x-2y%29=51%2840%29 Multiply the both sides of the first equation by 51.


153x-102y=2040 Distribute and multiply.


2%2885x%2B51y%29=2%28-70%29 Multiply the both sides of the second equation by 2.


170x%2B102y=-140 Distribute and multiply.


So we have the new system of equations:
system%28153x-102y=2040%2C170x%2B102y=-140%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:


%28153x-102y%29%2B%28170x%2B102y%29=%282040%29%2B%28-140%29


%28153x%2B170x%29%2B%28-102y%2B102y%29=2040%2B-140 Group like terms.


323x%2B0y=1900 Combine like terms.


323x=1900 Simplify.


x=%281900%29%2F%28323%29 Divide both sides by 323 to isolate x.


x=100%2F17 Reduce.


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153x-102y=2040 Now go back to the first equation.


153%28100%2F17%29-102y=2040 Plug in x=100%2F17.


900-102y=2040 Multiply.


-102y=2040-900 Subtract 900 from both sides.


-102y=1140 Combine like terms on the right side.


y=%281140%29%2F%28-102%29 Divide both sides by -102 to isolate y.


y=-190%2F17 Reduce.



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Answer:

So the solutions are x=100%2F17 and y=-190%2F17

which form the ordered pair