SOLUTION: Solve by elimination 8x-9y=24.5 7y-2x=-8.5

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Question 192047: Solve by elimination

8x-9y=24.5
7y-2x=-8.5


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

8x-9y=24.5 Start with the first equation.


80x-90y=245 Multiply EVERY term by 10 to make every number a whole number


7y-2x=-8.5 Move onto the second equation


-2x%2B7y=-8.5 Rearrange the terms.


-20x%2B70y=-85 Multiply EVERY term by 10 to make every number a whole number


So we have the system of equations:
system%2880x-90y=245%2C-20x%2B70y=-85%29


4%28-20x%2B70y%29=4%28-85%29 Multiply the both sides of the second equation by 4.


-80x%2B280y=-340 Distribute and multiply.


So we have the new system of equations:
system%2880x-90y=245%2C-80x%2B280y=-340%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:


%2880x-90y%29%2B%28-80x%2B280y%29=%28245%29%2B%28-340%29


%2880x%2B-80x%29%2B%28-90y%2B280y%29=245%2B-340 Group like terms.


0x%2B190y=-95 Combine like terms.


190y=-95 Simplify.


y=%28-95%29%2F%28190%29 Divide both sides by 190 to isolate y.


y=-1%2F2 Reduce.


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80x-90y=245 Now go back to the first equation.


80x-90%28-1%2F2%29=245 Plug in y=-1%2F2.


80x%2B45=245 Multiply.


80x=245-45 Subtract 45 from both sides.


80x=200 Combine like terms on the right side.


x=%28200%29%2F%2880%29 Divide both sides by 80 to isolate x.


x=5%2F2 Reduce.


So the solutions are x=5%2F2 and y=-1%2F2.


Which form the ordered pair .


This means that the system is consistent and independent.