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Question 106372: Hello out there,I really need some help with some problems,the first one is,State whether the system is consistent and independent,consistent and dependent,or inconsistent:4x+2y=8 and 2x+y=1.The next one is,State whether the system is consistent and independent,consistent and dependent,or inconsistent:x+y=4 and 2x-y=-7.The third one is,Determine whether the system has one solution,no solution,or infinitely many solutions:y=-x+2 and 3x+3y=6.And the last one is,Determine whether the system has one solution,no solution,or infinitely many solutions:y=2/3x and 2x-y=-4.Thanks to whoever can help.
Answer by elima(1433)   (Show Source):
You can put this solution on YOUR website! 4x+2y=8
2x+y=1
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We will solve this by elimination since you don't say which to use;
1)4x+2y=8
2)2x+y=1
we will multiply a -2 to the second equation to eliminate the y;
(-2)2x+y=1
-4x-2y=1
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Now lets add the two equations together;
4x+2y=8
-4x-2y=-2
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0=-2
Since this is o=-2, it is inconsistent
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With this next one, when you add them together they already eliminate a variable, so no other multiplying is necessary;
x+y=4
2x-y=-7
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3x=-3
x=-1
Now substitute the -1 for x in one of the equations;
-1+y=4
y=5
Since this has only one answer for x and y it is consistent and independent
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y=-x+2
3x+3y=6
x+y=2
-3x-3y=-6
3x+3y=6
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0=0
This is the same line so it is infinitely many solutions
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y=2/3x
2x-y=-4
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-2/3)x+y=0
2x-y=-4
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x=-3
y=-2
This has only one point, so it has only one solution
:)
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