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Mathematics 21 Online
OpenStudy (anonymous):

Solve by subsititution method or the add-or-minus-method

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

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...

OpenStudy (anonymous):

ohhhh.

OpenStudy (anonymous):

XD

OpenStudy (anonymous):

So then...

OpenStudy (anonymous):

b=-10/3

OpenStudy (anonymous):

-23/3,-1/3?

OpenStudy (anonymous):

-10/3*

OpenStudy (anonymous):

Right?... ><''

OpenStudy (unklerhaukus):

almost

OpenStudy (anonymous):

Grahhh. I suck at this. *ashamed*

OpenStudy (anonymous):

Let me try again.

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

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

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

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?

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

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?

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

hero (hero):

You're just now solving it?

OpenStudy (anonymous):

m hm..

OpenStudy (unklerhaukus):

thats right \[\large\color{red}\checkmark\]

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