## anonymous 3 years ago solve the system: y= -1/3 + 2 and x + 3y = 3

1. anonymous

-1/3x*

2. anonymous

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

3. anonymous

3y=-x+3?

4. anonymous

id set them both equal to y then solve like that

5. anonymous

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

6. anonymous

what?

7. 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$ ${x=3/2~~~~~~~~y=-5/2}$

8. 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

9. anonymous

oh sorry 1 second

10. 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$ $x=0~~~y=2$

11. anonymous

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

12. anonymous

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

13. anonymous

im so confused .-.

14. anonymous

its A

15. anonymous

how?

16. anonymous

y has to equal 1 when x is 0

17. jim_thompson5910

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

18. 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

19. anonymous

damn im confused...

20. anonymous

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

21. 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

22. anonymous

there is a no solution

23. 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)"

24. jim_thompson5910

so there must be a typo somewhere

25. anonymous

26. anonymous

i think i got this jim_thompson5910

27. anonymous

yeah i do thanks :)

28. 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. :-)

29. 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)

30. anonymous

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