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

1. trentsellars

-1/3x*

2. kmalone99

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

3. trentsellars

3y=-x+3?

4. katiebugg

id set them both equal to y then solve like that

5. kmalone99

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

6. trentsellars

what?

7. yummydum

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. trentsellars

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. yummydum

oh sorry 1 second

10. yummydum

$x+3(−1/3x+2)=3$ 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. yummydum

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

12. trentsellars

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

13. yummydum

im so confused .-.

14. yummydum

its A

15. trentsellars

how?

16. yummydum

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. kmalone99

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. trentsellars

damn im confused...

20. kmalone99

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

21. kmalone99

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. trentsellars

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. kmalone99

26. kmalone99

i think i got this jim_thompson5910

27. trentsellars

yeah i do thanks :)

28. kmalone99

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. kmalone99