Solve by subsititution method or the add-or-minus-method
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OpenStudy (anonymous):
\[\frac{ 1 }{ 3 }a-\frac{ 2 }{ 3 }b=1\]
OpenStudy (anonymous):
\[a+b+7=0\]
OpenStudy (anonymous):
Is the answer \[-\frac{ 19 }{ 3 }, -\frac{ 8 }{ 3 }\]
OpenStudy (unklerhaukus):
multiply our first equation by three
hero (hero):
Divide the second equation by -1/3
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OpenStudy (anonymous):
o3o...I just solved for a and i got a=2b+1...
OpenStudy (unklerhaukus):
almost
\[\frac{ 1 }{ 3 }a-\frac{ 2 }{ 3 }b=1\]
multiplying by three
\[a-2b=3\]
\[a=2b+3\]
, now substitute \(a\) into your second equation
\[a+b+7=0\]
\[(2b+3)+b+7=0\]
and solve for \(b\)
OpenStudy (anonymous):
How'd you get +3? ><''
OpenStudy (unklerhaukus):
one multiplied by three is three
OpenStudy (anonymous):
mk well first... i moved 2/3b to the other side...
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OpenStudy (anonymous):
ohhhh.
OpenStudy (anonymous):
XD
OpenStudy (anonymous):
So then...
OpenStudy (anonymous):
b=-10/3
OpenStudy (anonymous):
-23/3,-1/3?
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OpenStudy (anonymous):
-10/3*
OpenStudy (anonymous):
Right?... ><''
OpenStudy (unklerhaukus):
almost
OpenStudy (anonymous):
Grahhh. I suck at this. *ashamed*
OpenStudy (anonymous):
Let me try again.
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OpenStudy (anonymous):
mk...SO.
OpenStudy (anonymous):
2b+3+b+7=0.
OpenStudy (anonymous):
3b+10=0
3b=-10
b=-10/3
OpenStudy (unklerhaukus):
you got \(b\) right
OpenStudy (anonymous):
a=2(-10/3)+1
a=-20/3+1
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OpenStudy (anonymous):
and then....
OpenStudy (unklerhaukus):
\[a=2b+3\]
\[a=2\left(-\frac{10}3\right)+3\]
OpenStudy (anonymous):
ohhh. geez I see XD
OpenStudy (anonymous):
I'm a dumbcluck.
OpenStudy (unklerhaukus):
dont forget the three
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OpenStudy (anonymous):
-17/3 :P
OpenStudy (unklerhaukus):
not quite
OpenStudy (anonymous):
Arrgh.
OpenStudy (anonymous):
Wouldn't it turn out to be a=-20/3+3/3 though?
OpenStudy (unklerhaukus):
3=9/3
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OpenStudy (anonymous):
O3o...man...I'm really out of it today...omigod what's wrong with me...
OpenStudy (unklerhaukus):
Solving simultaneous equations is very tricky
OpenStudy (anonymous):
XD Thank you though. For fixing my dumbcluck-ness.
OpenStudy (anonymous):
So then....11/3 negative...
OpenStudy (anonymous):
Can I ask one more question?
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OpenStudy (unklerhaukus):
that is \(a\) !
OpenStudy (unklerhaukus):
, sure
OpenStudy (anonymous):
Okay so... the equations are...
OpenStudy (anonymous):
\[\frac{ 5a }{ 6 }-\frac{ b }{ 3 }=6\]
\[a+2b=0\]
OpenStudy (anonymous):
Okay so... a=-2b
5(-2b)/6-b/3
-10b/6-b/3=6
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OpenStudy (unklerhaukus):
that looks right so far
OpenStudy (anonymous):
mk...how to I solve -10b/6-b/3=6? I totally forgot.
OpenStudy (unklerhaukus):
\[-\frac{10}6b-\frac 13b=6\]
in the first fraction there is a common factor of 2 ,
cancel this,
then add the fractions
OpenStudy (anonymous):
Okay...
OpenStudy (anonymous):
-6b/3=6?
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OpenStudy (anonymous):
And then...
OpenStudy (anonymous):
I um...multiply both sides by 3.
OpenStudy (anonymous):
-3.
OpenStudy (unklerhaukus):
yeah \(b=-3\),
great work
what is \(a\)
OpenStudy (anonymous):
a=6
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