Question

I will award you! :)

How many solutions does the system of equations have?
-2=2x-4
y=-2/3x-1


A.
0
B.
1
C.
2
D.
infinite

Answer 1

Answer is F

Answer 2

@SolomonZelman

Answer 3

Are you sure you have written the system correctly ?

Answer 4

i wrote it wrong. one sec. :/ haha

Answer 5

2x+3y=6
y=-2/3x-1

Answer 6

\(\normalsize\color{blue}{ 2x+3y=6 }\)
\(\normalsize\color{blue}{ y=(-2/3)x-1 }\)

just want to play with the first equation a little bit to show you something.
\(\normalsize\color{blue}{ 2x+3y=6 }\)
\(\normalsize\color{blue}{ 3y=-2x+6 }\)
\(\normalsize\color{blue}{ y=(-2/3)x+2 }\)

so what you have is the following system above in red.
\(\normalsize\color{red}{ y=(-2/3)x+2 }\)
\(\normalsize\color{red}{ y=(-2/3)x-1 }\)

Answer 7

how many solutions can here be ?

Answer 8

two?

Answer 9

Okay, lets do this a little differently.

When I say

\(\normalsize\color{red}{ y=(-2/3)x-1 }\)
\(\normalsize\color{red}{ y=(-2/3)x+2 }\)

and when I say

\(\normalsize\color{blue}{ y+(2/3)x=-1 }\)
\(\normalsize\color{blue}{ y+(2/3)x=2 }\)

I am not changing anything, right?

Answer 10

right.

Answer 11

Now, here the problem arises.

In the first equation ( \(\normalsize\color{blue}{ y+(2/3)x=-1 }\) ) we see that
`y+(2/3)x` is equal to `1`
but in the second equation we see that this same number (which is `y+(2/3)x` ) is equal to 2.

Can the same number be equal to -1 and to 2 at the same time ?

Answer 12

absolutely not.

Answer 13

correct, and that means that there are no solutions.... correct:)

Answer 14

no solutions is same as zero solutions.

Answer 15

thank you so much! you helped me out so much just in the nic of time! :)

Answer 16

Anytime! Btw, where do you live? I can guess somewhere south from the equator since you have school, but where if not a secret? (just wondering)

Answer 17

Pennsylvania. summer school.. :/

Answer 18

Ohh... I see:) I live in Atlanta GA (absolute silence and good weather)
anyway, good luck with your summer school !

Answer 19

Ah! i love Georgia. well, thanks again and have a good summer! :)

Answer 20

I'm fairly certain that i'll call upon you again for help.

Answer 21

You too: good summer:) YOu are probably finishing your summer school right now, so have a good real summer, after your school summer.

Answer 22

haha, not quite yet.. i finish in about one month.. by which point i'm starting regular school. :(