Question 106372
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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{{{(4/3)x=-4}}}
x=-3
{{{y=(2/3)(-3)}}}
y=-2
This has only one point, so it has only one solution
:)