SOLUTION: hi, i need exactly step by step solution using elimination method and check.thank u. 4x+y=1 x-2y=-2

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Question 147704This question is from textbook
: hi, i need exactly step by step solution using elimination method and check.thank u.
4x+y=1
x-2y=-2 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system of equations:
system%284x%2By=1%2Cx-2y=-2%29


2%284x%2By%29=2%281%29 Multiply the both sides of the first equation by 2.


8x%2B2y=2 Distribute and multiply.


So we have the new system of equations:
system%288x%2B2y=2%2Cx-2y=-2%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:


%288x%2B2y%29%2B%28x-2y%29=%282%29%2B%28-2%29


%288x%2B1x%29%2B%282y%2B-2y%29=2%2B-2 Group like terms.


9x%2B0y=0 Combine like terms. Notice how the y terms cancel out.


9x=0 Simplify.


x=%280%29%2F%289%29 Divide both sides by 9 to isolate x.


x=0 Reduce.


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8x%2B2y=2 Now go back to the first equation.


8%280%29%2B2y=2 Plug in x=0.


0%2B2y=2 Multiply.


2y=2 Remove any zero terms.


y=%282%29%2F%282%29 Divide both sides by 2 to isolate y.


y=1 Reduce.


So our answer is x=0 and y=1.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 4x%2By=1 (red) and x-2y=-2 (green)


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Check:


4x%2By=1 Start with the first equation.


4%2A%280%29%2B%281%29=1 Plug in x=0 and y=1.


1=1 Evaluate and simplify the left side.


Since the equation is true, this means that (0,1) is a solution for the first equation.


x-2y=-2 Start with the second equation.


%280%29-2%2A%281%29=-2 Plug in x=0 and y=1.


-2=-2 Evaluate and simplify the left side.


Since the equation is true, this means that (0,1) is a solution for the second equation.


Since all of the equations of the system are true, this means that (0,1) is a solution of the system. So this verifies our answer.