SOLUTION: solve by substitution or elimination method. classify as consistent, inconsistent, or dependent and independent 4x-7y = 29 2x+5y = -11 thank you!!

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Question 177839: solve by substitution or elimination method. classify as consistent, inconsistent, or dependent and independent

4x-7y = 29
2x+5y = -11

thank you!!
Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
elimination is almost always easier in my opinion:
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what you are doing in elimination, also call addition or subtraction, is trying to manipulate the equations so that you can eliminate one variable
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4x-7y=29......eq 1
2x+5y=-11.....eq 2
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I try to write these so the terms all line up, because it is much easier to see what is taking place. In this set of equations we either eliminate the x or y terms to eliminate the x terms we would multiply eq 2 by -2 and add the 2 equations together. To eliminate the y terms we would have to multiply eq 1 by 5 and eq 2 by 7. It is obviously easier to go with the elimination of the x terms since we only have to multiply out one equation.
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so eq 2 when multiplied by -2 results in -2(2x+5y=-11)--->-4x-10y=22. now lets take this revised eq 2 and place it directily under eq 1 that did not have to be manipulated
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4x-7y=29......eq 1
-4x-10y=22....eq 2 revised
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now we need to add these two equations together. It is easy to see with these equations lined up that the x terms will be eliminated because 4x-4x=0. We are left with -7y-10y=29+22
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-17y=51
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now take y's found value and plug it back into any numbered equation we have and solve for x. I choose eq 1.
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4x-7(-3) = 29
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4x+21=29
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4x=8
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