SOLUTION: 2x-4y=6 and 4x+y=21 work addition method and is it independent, inconsistent or dependent.

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Question 319710: 2x-4y=6 and 4x+y=21 work addition method and is it independent, inconsistent or dependent.
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%282x-4y=6%2C4x%2By=21%29


4%284x%2By%29=4%2821%29 Multiply the both sides of the second equation by 4.


16x%2B4y=84 Distribute and multiply.


So we have the new system of equations:
system%282x-4y=6%2C16x%2B4y=84%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:


%282x-4y%29%2B%2816x%2B4y%29=%286%29%2B%2884%29


%282x%2B16x%29%2B%28-4y%2B4y%29=6%2B84 Group like terms.


18x%2B0y=90 Combine like terms.


18x=90 Simplify.


x=%2890%29%2F%2818%29 Divide both sides by 18 to isolate x.


x=5 Reduce.


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2x-4y=6 Now go back to the first equation.


2%285%29-4y=6 Plug in x=5.


10-4y=6 Multiply.


-4y=6-10 Subtract 10 from both sides.


-4y=-4 Combine like terms on the right side.


y=%28-4%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=1 Reduce.


So the solutions are x=5 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 2x-4y=6 (red) and 4x%2By=21 (green)