SOLUTION: Please help me solve this system by substitution? { 2x - y = 4 { y = 2x - 4

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Question 688349: Please help me solve this system by substitution? { 2x - y = 4
{ y = 2x - 4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

2x+-+y+=+4........1
y+=+2x+-+4..........2
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2x+-+y+=+4......1....solve for y
2x%2B4+=y.......substitute in 2
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2x%2B4++=+2x+-+4..........2....solve for x
2x-2x=+-4+-+4
0=+-8............. there are an infinite number of solutions and the
system is dependent

check it graphically:
2x+-+y+=+4........1
y+=+2x+-+4..........2
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2x+-+y+=+4........1
-2x%2By+=-4..........2
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Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


2x-y=4

-2x%2By=-4





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


2x-y=4 Start with the given equation



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



-y=-2x%2B4 Rearrange the equation



y=%28-2x%2B4%29%2F%28-1%29 Divide both sides by -1



y=%28-2%2F-1%29x%2B%284%29%2F%28-1%29 Break up the fraction



y=2x-4 Reduce



Now lets graph y=2x-4 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x-4%29+ Graph of y=2x-4




So let's solve for y on the second equation


-2x%2By=-4 Start with the given equation



1y=-4%2B2x Add 2+x to both sides



1y=%2B2x-4 Rearrange the equation



y=%28%2B2x-4%29%2F%281%29 Divide both sides by 1



y=%28%2B2%2F1%29x%2B%28-4%29%2F%281%29 Break up the fraction



y=2x-4 Reduce





Now lets add the graph of y=2x-4 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x-4%2C2x-4%29+ Graph of y=2x-4(red) and y=2x-4(green)


From the graph, we can see that the two lines are identical (one lies perfectly on top of the other) and intersect at all points of both lines. So there are an infinite number of solutions and the system is dependent.