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

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

Mathematics
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-1/3x*
x+3y=3 substrct x from both sides what would you get?
3y=-x+3?

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id set them both equal to y then solve like that
ar you can sub y=-1/3x+2 in to other equation x+3(-1/3 x+x)=3 solve for x
what?
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:\[y=-1/3(3/2)+2\]\[y=-1/2+2\]\[y=-5/2\] \[{x=3/2~~~~~~~~y=-5/2}\]
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
oh sorry 1 second
\[x+3(−1/3x+2)=3\] and then solve for x: \[x−x+6=3\]\[0x+6=3\]\[0x=−3\]\[x=0\] now substitute this x into the first equation: \[y=−1/3(0)+2\]\[y=0+2\]\[y=2\] \[x=0~~~y=2\]
is that one of the choices? sorry i did that wrong but i fixed it...helpful? :)
(0, 1) (1, 0) (3, 1/3) (3/2, 0) these are the options.
im so confused .-.
its A
how?
y has to equal 1 when x is 0
yummydum, if 0x=−3, then 0 = -3 which is a contradiction So there are no solutions.
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
damn im confused...
is that all the possiablities? there is no solutions be these are parallal lines
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
there is a no solution
i would be confused too...the answer choices are incorrect because the true answer is "no solution" or "there is/are no solution(s)"
so there must be a typo somewhere
there is your answer but do you understand why?
i think i got this jim_thompson5910
yeah i do thanks :)
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)
already said this phi

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