Question

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.

Answer 1

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

Answer 2

the second equation is written in the standard form. So let us change the first equation also into standard form. Can you do that?

Answer 3

@bookworm00981

Answer 4

I think. @rajee_sam

Answer 5

Ok lets write it then

Answer 6

We simplify it right. combine like terms?

Answer 7

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

Answer 8

Ok, let me try.

Answer 9

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

Answer 10

now rewrite it

Answer 11

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

Answer 12

no I am here

Answer 13

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

Answer 14

Haha I do that too.

Answer 15

are you doing this?

Answer 16

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

Answer 17

Trying..

Answer 18

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

Answer 19

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

Answer 20

\[y = -\frac{ 2 }{ 3 }x + 3\]\[3y = 3 (-\frac{ 2 }{ 3 } x + 3)\]\[3y = -2x +9\]Bring the -2x to the other side. \[2x + 3y = 9\]

Answer 21

yes

Answer 22

Ok, let me give it a go.

Answer 23

now what do you see in both equations?

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

Ok, so did we flip the equation?

Answer 28

you sound lost?

Answer 29

yes..... T_T

Answer 30

sorry lost connection for a sec.

Answer 31

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.

Answer 32

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

Answer 33

I am not going to do anything to eqn. 2 for now.

Now let us focus on Eqn 1

Answer 34

Eqn mean equation?

Answer 35

yes

Answer 36

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

Answer 37

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

Answer 38

I have to get rid of the fractions too

Answer 39

so what do I do?

Answer 40

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

Answer 41

Umm...

Answer 42

Now your first eqn. has been rewritten as

2x + 3y = 9

Did you get that part?

Answer 43

Looking at your work trying too.

Answer 44

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

Answer 45

-2/3

Answer 46

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

Answer 47

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

Answer 48

I thought I said that earlier? Oh well.

Answer 49

And I said yes to that And you wandered off after that So lets move on to the next.

Did you understand upto now?

Answer 50

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

2x + 3y = 9

Answer 51

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

Answer 52

not to fret.

Answer 53

You are doing good

Answer 54

So now I have two equations.

Eqn 1

2x + 3y = 9

Eqn . 2

2x + 3y = 9

Answer 55

What can you say about them both?

Answer 56

They are alike.

Answer 57

They are the same

Answer 58

So they will have infinitely many solutions

Answer 59

Oh. so they are are parallel.

Answer 60

They are infact the same line

Answer 61

Thanks.

Answer 62

yw

Answer 63

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)