ValentinaT
Using substitution, could someone please help me with this system?
–y + 3x = 6
y = –6x + 12
So far I've gotten:
Substituting the second equation into the first you get
-(-6x+12) + 3x = 6
Which can be solved for x after finding x you can use the second equation above directly to find y
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MathDad72
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Sounds like you know what you are doing .... What's the problem you are having?
ValentinaT
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Well, I had help with that part, but I can't figure out what to do next. I tried using my textbook, but it was a bit confusing, because they showed you what to do, but didn't explain it.
MathDad72
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Ok, first let's distribute that -(-6x+12)
Can you do that?
ValentinaT
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-6x + -72?
MathDad72
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Think of it this way:
(-)(-6x) & (-)(12)
ValentinaT
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Because negative times negative equals a positive 6x + -12?
MathDad72
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yes, very good
so we have
6x-12+3x=6
What will you do next?
ValentinaT
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Add 6x and 3x?
MathDad72
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correct
9x-12=6
now what?
ValentinaT
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Substitute for y from the other equation?
MathDad72
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Let's try to solve for x.
ValentinaT
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Sorry, I was looking at my textbook, and thought that we were onto that step.
MathDad72
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:-)
That's ok.
ValentinaT
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Okay, so how would I go about solving for x? Also, thank you for the medal.
MathDad72
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We have x on one side, can we get non x-values on the other side?
ValentinaT
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You would add 12 + 6? Then get 18, divided by 9x would equal 2.
MathDad72
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Excellent:
So x=2
ValentinaT
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Okay.
MathDad72
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What are you going to do with that x=2?
MathDad72
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You still there?
ValentinaT
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Substitute 2 for x in either equation and solve for y? Sorry, my computer is slow sometimes.
MathDad72
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Heh I Understand.
You are correct, good job!
ValentinaT
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Thank you! So, -y + 3(2) + 6.
MathDad72
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-y+3(2)=6
ValentinaT
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So, -y + 6 = 6.
MathDad72
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correct
ValentinaT
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What would I do next?
MathDad72
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same that you did when you had 9x-12=6 and solved for x. now we are going to it for y
ValentinaT
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6 - 6 = 0 So y, would be 0?
MathDad72
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That is correct.
ValentinaT
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Then I would substitute 0for y, and get 0 + 6 = 6.
MathDad72
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Correct:
So your Answer is:
X=2, y=0
MathDad72
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As long as you get a correct statement when you plug them both back in, like you showed 6=6 and not get something like 7=6, then we would have a problem.
ValentinaT
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Okay, thank you some much for your help. If I could give you more than one medal I would.
MathDad72
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Thank you,
It is nice to meet someone who wants to work out the problems and not just demand an answer.
ValentinaT
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I get what you mean, you are a very good teacher by the way.