SOLUTION: Solve the given system by use of elimination: 4x-9y=10.5 7y-2x=-6.5

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the given system by use of elimination: 4x-9y=10.5 7y-2x=-6.5       Log On


   

Question 202424: Solve the given system by use of elimination:

4x-9y=10.5
7y-2x=-6.5



Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4x-9y=10.5 Start with the first equation.


10%284x%29-10%289y%29=10%2810.5%29 Multiply EVERY term by 10 to make every value a whole number.


40x-90y=105 Multiply.


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7y-2x=-6.5 Move onto the second equation.


-2x%2B7y=-6.5 Rearrange the terms.


10%28-2x%29%2B10%287y%29=10%28-6.5%29 Multiply EVERY term by 10 to make every value a whole number.


-20x%2B70y=-65 Multiply.



So we have the given system of equations:

system%2840x-90y=105%2C-20x%2B70y=-65%29


2%28-20x%2B70y%29=2%28-65%29 Multiply the both sides of the second equation by 2.


-40x%2B140y=-130 Distribute and multiply.


So we have the new system of equations:

system%2840x-90y=105%2C-40x%2B140y=-130%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:


%2840x-90y%29%2B%28-40x%2B140y%29=%28105%29%2B%28-130%29


%2840x-40x%29%2B%28-90y%2B140y%29=105%2B-130 Group like terms.


0x%2B50y=-25 Combine like terms.


50y=-25 Simplify.


y=%28-25%29%2F%2850%29 Divide both sides by 50 to isolate y.


y=-1%2F2 Reduce.


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40x-90y=105 Now go back to the first equation.


40x-90%28-1%2F2%29=105 Plug in y=-1%2F2.


40x%2B45=105 Multiply.


40x=105-45 Subtract 45 from both sides.


40x=60 Combine like terms on the right side.


x=%2860%29%2F%2840%29 Divide both sides by 40 to isolate x.


x=3%2F2 Reduce.


So the solutions are x=3%2F2 and y=-1%2F2.


Which form the ordered pair .


This means that the system is consistent and independent.