SOLUTION: Solve the system using any algebraic method. x-y=17 1/2x-3y=1

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Question 215116: Solve the system using any algebraic method.
x-y=17
1/2x-3y=1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F2%29x-3y=1 Start with the second equation.


x-6y=2 Multiply EVERY term by the LCD 2 to clear out the fraction.


So we have the system of equations:


system%28x-y=17%2Cx-6y=2%29


x-y=17 Start with the first equation.


-y=17-x Subtract x from both sides.


y=%2817-x%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=x-17 Rearrange the terms and simplify.


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x-6y=2 Move onto the second equation.


x-6%28x-17%29=2 Now plug in y=x-17.


x-6x%2B102=2 Distribute.


-5x%2B102=2 Combine like terms on the left side.


-5x=2-102 Subtract 102 from both sides.


-5x=-100 Combine like terms on the right side.


x=%28-100%29%2F%28-5%29 Divide both sides by -5 to isolate x.


x=20 Reduce.


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Since we know that x=20, we can use this to find y.


x-y=17 Go back to the first equation.


1%2820%29-y=17 Plug in x=20.


20-y=17 Multiply.


-y=17-20 Subtract 20 from both sides.


-y=-3 Combine like terms on the right side.


y=%28-3%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=3 Reduce.


So the solutions are x=20 and y=3.


This means that the system is consistent and independent.