SOLUTION: 2x-4y=7 4x+2y=-1

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Question 122678: 2x-4y=7
4x+2y=-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to solve this using substitution?





Start with the given system of equations:

system%282x-4y=7%2C4x%2B2y=-1%29



Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

2x-4y=7 Start with the first equation


-4y=7-2x Subtract 2x from both sides


-4y=-2x%2B7 Rearrange the equation


y=%28-2x%2B7%29%2F%28-4%29 Divide both sides by -4


y=%28%28-2%29%2F%28-4%29%29x%2B%287%29%2F%28-4%29 Break up the fraction


y=%281%2F2%29x-7%2F4 Reduce



Since y=%281%2F2%29x-7%2F4, we can now replace each y in the second equation with %281%2F2%29x-7%2F4 to solve for x



4x%2B2highlight%28%28%281%2F2%29x-7%2F4%29%29=-1 For the second equation, replace y with %281%2F2%29x-7%2F4. Since this eliminates y, we can now solve for x.



4x%2B%282%29%281%2F2%29x%2B%282%29%28-7%2F4%29=-1 Distribute 2 to %281%2F2%29x-7%2F4


4x%2B%282%2F2%29x-14%2F4=-1 Multiply


%284%29%284x%2B%282%2F2%29x-14%2F4%29=%284%29%28-1%29 Multiply both sides by the LCM of 4. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



16x%2B4x-14=-4 Distribute and multiply the LCM to each side



20x-14=-4 Combine like terms on the left side


20x=-4%2B14Add 14 to both sides


20x=10 Combine like terms on the right side


x=%2810%29%2F%2820%29 Divide both sides by 20 to isolate x



x=1%2F2 Reduce





-----------------First Answer------------------------------


So the first part of our answer is: x=1%2F2


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Since we know that x=1%2F2 we can plug it into the equation y=%281%2F2%29x-7%2F4 (remember we previously solved for y in the first equation).



y=%281%2F2%29x-7%2F4 Start with the equation where y was previously isolated.


y=%281%2F2%29%281%2F2%29-7%2F4 Plug in x=1%2F2


y=1%2F4-7%2F4 Multiply


y=-3%2F2 Combine like terms and reduce. (note: if you need help with fractions, check out this solver)



-----------------Second Answer------------------------------


So the second part of our answer is: y=-3%2F2


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-----------------Summary------------------------------

So our answers are:

x=1%2F2 and y=-3%2F2

which form the point


which as an ordered pair, look like:




Notice if we graph the equations (if you need help with graphing, check out this solver)
2x-4y=7
4x%2B2y=-1
we get


graph of 2x-4y=7 (red) and 4x%2B2y=-1 (green) and the intersection of the lines (blue circle).

and we can see that the two equations intersect at . This verifies our answer.