solve the system: y= -1/3 + 2 and x + 3y = 3

- anonymous

solve the system: y= -1/3 + 2 and x + 3y = 3

- jamiebookeater

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- anonymous

-1/3x*

- anonymous

x+3y=3 substrct x from both sides what would you get?

- anonymous

3y=-x+3?

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## More answers

- anonymous

id set them both equal to y then solve like that

- anonymous

ar you can sub y=-1/3x+2
in to other equation
x+3(-1/3 x+x)=3
solve for x

- anonymous

what?

- anonymous

since y equals -1/3x+2 we can substitute that into the second equation like this:\[x+3(-1/3 x+2)=3\]and then solve for x:\[x-3x+6=3\]\[-2x+6=3\]\[-2x=-3\]\[x=3/2\]
now substitute this x into the first equation:\[y=-1/3(3/2)+2\]\[y=-1/2+2\]\[y=-5/2\]
\[{x=3/2~~~~~~~~y=-5/2}\]

- anonymous

okay I see the first part. but the problem with -5/2, is that thats not one of the answer options. but 3/2, 0 is

- anonymous

oh sorry 1 second

- anonymous

\[x+3(−1/3x+2)=3\]
and then solve for x:
\[x−x+6=3\]\[0x+6=3\]\[0x=−3\]\[x=0\]
now substitute this x into the first equation:
\[y=−1/3(0)+2\]\[y=0+2\]\[y=2\]
\[x=0~~~y=2\]

- anonymous

is that one of the choices? sorry i did that wrong but i fixed it...helpful? :)

- anonymous

(0, 1)
(1, 0)
(3, 1/3)
(3/2, 0)
these are the options.

- anonymous

im so confused .-.

- anonymous

its A

- anonymous

how?

- anonymous

y has to equal 1 when x is 0

- jim_thompson5910

yummydum, if 0x=−3, then 0 = -3 which is a contradiction
So there are no solutions.

- anonymous

besides the mistake then you .. wait
if you have choses then the order pair are (x,y)
sub into the equations
example take the first one 0,1
y= -1/3 + 2 and x + 3y = 3
1=-1/3(0)+2 and 0+3(1)=3
1=2 not a solutation and 3=3 solves right equations
so do the next set of pairs and tell me what you find out

- anonymous

damn im confused...

- anonymous

is that all the possiablities? there is no solutions be these are parallal lines

- anonymous

sorry your confused but it says solve so look at what we have
sub the points in the equations and see if it equals or solve for x or y and then find what you did nt solve for... do you understand this

- anonymous

there is a no solution

- jim_thompson5910

i would be confused too...the answer choices are incorrect because the true answer is "no solution" or "there is/are no solution(s)"

- jim_thompson5910

so there must be a typo somewhere

- anonymous

there is your answer but do you understand why?

- anonymous

i think i got this jim_thompson5910

- anonymous

yeah i do thanks :)

- anonymous

great
you also can see let equations equal
-1/3 x+2=-1/3 x+1and solve for x
then you get 2=1 so no solution. :-)

- phi

another way to look at
\[y= -\frac{1}{3}x + 2 \text { and } x + 3y = 3\]
the 2nd equation, after rearranging into y= mx+b form is
\[ y= -\frac{1}{3}x+3\]
You have two lines that are parallel, and never meet.
There is no (x,y) pair that is on both lines (as would be the case if they intersected)

- anonymous

already said this phi

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