Question 417563: dont understand this problem and solution teacher put on board could you help me understand? I dont get it.
4y=2x-10
2y=2(5+2y)-10
4y=10+4y-10
4y-4y=10-10
0=0
=
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! dont understand this problem and solution teacher put on board could you help me understand? I dont get it.
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I think you missed a line that was on the board:
x = 5+2y
4y = 2x-10
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Substituting for "x" you get the following:
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4y=2x-10
4y=2(5+2y)-10
4y=10+4y-10
4y-4y=10-10
0=0
----
Conclusion:
The system of equations is true for all values of x.
The two equation are really the same equation.
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Cheers,
Stan H.
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Answer by josmiceli(19441)  (Show Source):
You can put this solution on YOUR website! 4y=2x-10
4y=2(5+2y)-10
4y=10+4y-10
4y-4y=10-10
0=0
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I get what what the teacher has in mind. At the beginning, there
must have been 2 equations:
(1) 
and
(2) 
What the teacher was trying to show is that these equations are
exactly the same. (S)he did this by trying to "solve" for x and y
in the normal way, by substitution. If the equations were different,
this would have resulted in a solution (x,y).
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To show the equations are the same, subtract  from both sides
of (2). Then you have:
(2) 
Now multiply both sides by 
(2)
So, if both equations are the same, there is no solution. Also if the
equations are different, but have the same slope, tyhere can be no
solution, since they would be parallel lines that never meet.
An example would be:
(1) 
(2) 
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