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.

- anonymous

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- 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

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

@bookworm00981

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

I think. @rajee_sam

- rajee_sam

Ok lets write it then

- anonymous

We simplify it right. combine like terms?

- 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

Ok, let me try.

- rajee_sam

\[y = -\frac{ 2 }{ 3 }x +3\]

- rajee_sam

now rewrite it

- anonymous

I just went Blank... don't leave let me think for a second.

- rajee_sam

no I am here

- 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

Haha I do that too.

- rajee_sam

are you doing this?

- rajee_sam

you need to focus on this. You can help others later

- anonymous

Trying..

- anonymous

I can do math, i just can't remember the steps.

- anonymous

Ok, am I supposed to multiply by three on both sides?

- 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

yes

- anonymous

Ok, let me give it a go.

- rajee_sam

now what do you see in both equations?

- anonymous

Ah drat, I cant draw on the equation like if it was a drawing...

- anonymous

I see three's on both sides...???

- 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

Ok, so did we flip the equation?

- rajee_sam

you sound lost?

- anonymous

yes..... T_T

- anonymous

sorry lost connection for a sec.

- 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

Eqn. 1 \[y = -\frac{ 2 }{ 3 }x + 3\] Eqn. 2 \[2x + 3y = 9\]

- rajee_sam

I am not going to do anything to eqn. 2 for now.
Now let us focus on Eqn 1

- anonymous

Eqn mean equation?

- rajee_sam

yes

- rajee_sam

So eqn. 1 I have to rewrite in standard form.

- anonymous

Ok, let me. 2/3x+y=3?

- rajee_sam

I have to get rid of the fractions too

- rajee_sam

so what do I do?

- rajee_sam

\[y = -\frac{ 2 }{ 3 }x + 3\]\[3y = 3 (-\frac{ 2 }{ 3 }x + 3 )\]\[3y = -2x + 9\]\[2x + 3y = 9\]

- anonymous

Umm...

- rajee_sam

Now your first eqn. has been rewritten as
2x + 3y = 9
Did you get that part?

- anonymous

Looking at your work trying too.

- rajee_sam

1st step was to get rid of the fraction in front of x

- rajee_sam

-2/3

- rajee_sam

multiply both sides of the equation by 3 ( The denominator)

- rajee_sam

3y = 3(-2/3 x + 3)

- anonymous

I thought I said that earlier? Oh well.

- 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

how I rewrote y = -2/3x + 3 as
2x + 3y = 9

- anonymous

Fairly well I suppose. I excell in all other subjects, yet I am like a child before confusing Algebra.

- rajee_sam

not to fret.

- rajee_sam

You are doing good

- rajee_sam

So now I have two equations.
Eqn 1
2x + 3y = 9
Eqn . 2
2x + 3y = 9

- rajee_sam

What can you say about them both?

- anonymous

They are alike.

- rajee_sam

They are the same

- rajee_sam

So they will have infinitely many solutions

- anonymous

Oh. so they are are parallel.

- rajee_sam

They are infact the same line

- anonymous

Thanks.

- rajee_sam

yw

- 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)

Looking for something else?

Not the answer you are looking for? Search for more explanations.