anonymous
  • anonymous
Have a couple of questions on a timed Math Quiz that I don't Understand, Please Help me to understand, Please be patient also. They will be in comment.
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
How many solutions does the following system have? y = -2/3 x + 3 and 2x + 3y = 9 one solution no solution infinitely many solutions cannot be determined
rajee_sam
  • rajee_sam
the second equation is written in the standard form. So let us change the first equation also into standard form. Can you do that?
rajee_sam
  • rajee_sam
@bookworm00981

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anonymous
  • anonymous
I think. @rajee_sam
rajee_sam
  • rajee_sam
Ok lets write it then
anonymous
  • anonymous
We simplify it right. combine like terms?
rajee_sam
  • rajee_sam
there are no like terms. We have to write it like Ax + By = C. Bringing x and y together and getting rid of the fraction and make it look just like the second equation
anonymous
  • anonymous
Ok, let me try.
rajee_sam
  • rajee_sam
\[y = -\frac{ 2 }{ 3 }x +3\]
rajee_sam
  • rajee_sam
now rewrite it
anonymous
  • anonymous
I just went Blank... don't leave let me think for a second.
rajee_sam
  • rajee_sam
no I am here
rajee_sam
  • rajee_sam
I help 2 - 3 people at a time. So Even if I go in and out I will see to it that you get this
anonymous
  • anonymous
Haha I do that too.
rajee_sam
  • rajee_sam
are you doing this?
rajee_sam
  • rajee_sam
you need to focus on this. You can help others later
anonymous
  • anonymous
Trying..
anonymous
  • anonymous
I can do math, i just can't remember the steps.
anonymous
  • anonymous
Ok, am I supposed to multiply by three on both sides?
rajee_sam
  • rajee_sam
\[y = -\frac{ 2 }{ 3 }x + 3\]\[3y = 3 (-\frac{ 2 }{ 3 } x + 3)\]\[3y = -2x +9\]Bring the -2x to the other side. \[2x + 3y = 9\]
rajee_sam
  • rajee_sam
yes
anonymous
  • anonymous
Ok, let me give it a go.
rajee_sam
  • rajee_sam
now what do you see in both equations?
anonymous
  • anonymous
Ah drat, I cant draw on the equation like if it was a drawing...
anonymous
  • anonymous
I see three's on both sides...???
rajee_sam
  • rajee_sam
The first equation when I rewrote in standard form turned out to be 2x + 3y = 9 My second equation is 2x + 3y = 9 as well
anonymous
  • anonymous
Ok, so did we flip the equation?
rajee_sam
  • rajee_sam
you sound lost?
anonymous
  • anonymous
yes..... T_T
anonymous
  • anonymous
sorry lost connection for a sec.
rajee_sam
  • rajee_sam
Let me start over. Focus and ditch your friend for a few minutes. She will live. We have two equations given to us. Both are linear. First equation is in Slope-intercept form and the second one is in Standard form. For solving system of equations we need to have the equations in standard form.
rajee_sam
  • rajee_sam
Eqn. 1 \[y = -\frac{ 2 }{ 3 }x + 3\] Eqn. 2 \[2x + 3y = 9\]
rajee_sam
  • rajee_sam
I am not going to do anything to eqn. 2 for now. Now let us focus on Eqn 1
anonymous
  • anonymous
Eqn mean equation?
rajee_sam
  • rajee_sam
yes
rajee_sam
  • rajee_sam
So eqn. 1 I have to rewrite in standard form.
anonymous
  • anonymous
Ok, let me. 2/3x+y=3?
rajee_sam
  • rajee_sam
I have to get rid of the fractions too
rajee_sam
  • rajee_sam
so what do I do?
rajee_sam
  • rajee_sam
\[y = -\frac{ 2 }{ 3 }x + 3\]\[3y = 3 (-\frac{ 2 }{ 3 }x + 3 )\]\[3y = -2x + 9\]\[2x + 3y = 9\]
anonymous
  • anonymous
Umm...
rajee_sam
  • rajee_sam
Now your first eqn. has been rewritten as 2x + 3y = 9 Did you get that part?
anonymous
  • anonymous
Looking at your work trying too.
rajee_sam
  • rajee_sam
1st step was to get rid of the fraction in front of x
rajee_sam
  • rajee_sam
-2/3
rajee_sam
  • rajee_sam
multiply both sides of the equation by 3 ( The denominator)
rajee_sam
  • rajee_sam
3y = 3(-2/3 x + 3)
anonymous
  • anonymous
I thought I said that earlier? Oh well.
rajee_sam
  • rajee_sam
And I said yes to that And you wandered off after that So lets move on to the next. Did you understand upto now?
rajee_sam
  • rajee_sam
how I rewrote y = -2/3x + 3 as 2x + 3y = 9
anonymous
  • anonymous
Fairly well I suppose. I excell in all other subjects, yet I am like a child before confusing Algebra.
rajee_sam
  • rajee_sam
not to fret.
rajee_sam
  • rajee_sam
You are doing good
rajee_sam
  • rajee_sam
So now I have two equations. Eqn 1 2x + 3y = 9 Eqn . 2 2x + 3y = 9
rajee_sam
  • rajee_sam
What can you say about them both?
anonymous
  • anonymous
They are alike.
rajee_sam
  • rajee_sam
They are the same
rajee_sam
  • rajee_sam
So they will have infinitely many solutions
anonymous
  • anonymous
Oh. so they are are parallel.
rajee_sam
  • rajee_sam
They are infact the same line
anonymous
  • anonymous
Thanks.
rajee_sam
  • rajee_sam
yw
phi
  • phi
Another way to do this problem (probably the way they expect you to solve it) is put both equations in slope-intercept form: y = -2/3 x + 3 and 2x + 3y = 9 become \[ y= -\frac{2}{3}x +3 \\ y= -\frac{2}{3}x +3 \] they are the same line, and lay on top on one another, so you get an infinite number of solutions. If they had the same slope, and different y intercepts, they would be parallel and never intersect, hence no solution if they have different slopes, the lines will meet somewhere, and there is one solution (where they meet)

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