## anonymous 4 years ago Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. 4x-8y=48 11x+3y=-105.5

1. campbell_st

simplify 4x - 8y = 48 to x - 2y = 12 (1) and 11x + 3y = -105.5 (2) then use (1) x 11 - (2) which will eliminate x and solve for y

2. anonymous

yikes another one with decimals!

3. anonymous

you got this?

4. anonymous

no not really

5. anonymous

hold on we can do it

6. anonymous

$x - 2y = 12$ $11x+3y=-105.5$

7. anonymous

multiply the first equation by -11 and add to the second one

8. anonymous

ok is it 2y or 3y

9. anonymous

$-11x+22y=132$ $11x+3y=-105.5$

10. anonymous

is it suppose to be x-2y or x-3y?

11. anonymous

first equation simplifies by dividing by 4, giving you $x-2y=12$

12. anonymous

oh ok

13. anonymous

now add the two equations together

14. anonymous

the x terms add up to zero and you get $25y=26.5$ if my arithmetic is correct

15. anonymous

damn i screwed up again!

16. anonymous

ok lol we can fix it

17. anonymous

you multiply the first one by -11

18. anonymous

$-11x+22y=-132$

19. anonymous

i forgot the negative on the right hand side

20. anonymous

ok so where does that come in

21. anonymous

$-11x+22y=-132$ $11x+3y=-105.5$

22. anonymous

ok lets go slow

23. anonymous

you have $x-2y=12$ $11x+3y=-105.5$ right?

24. anonymous

ok

25. anonymous

and you want to eliminate one of the variables so you can solve on equation with one variable

26. anonymous

i am confused on what comes first can you lay it out the way it suppose to be

27. anonymous

yes it looks like this

28. anonymous

ok

29. anonymous

$x-2y=12$ $11x+3y=-105.5$ then $(-11)\times (x-2y)=(-11)\times 12$ $11x+3y=-105.5$ then $-11x+22y=-132$ $11x+3y=-105.5$

30. anonymous

you have to figure out for yourself that if you multiply the first equation across by -11 and then add, the x terms will drop out when you add the two equations. finding what to multiply by is up to you.

31. anonymous

i am lost

32. anonymous

now add and get $25y=-235.5$ so now $x=-237.5\div 25=-9.5$

33. anonymous

why don't we try an easy one first. suppose i see $x+y=1$ $x-y=7$how can i find x and y?

34. anonymous

if you add the two equations together you get $2x=8$ because you get $x+y+x-y=1+7$ $2x=8$

35. anonymous

ok

36. anonymous

now i have one variable and one equation, so easy to solve, if $2x=8$ then $x=4$ and if i know $x=4$ then i know $y=3$ because the first equation says $x+y=7$ so $4+y=7$ and therefore $y=3$

37. anonymous

unfortunately in your problem if i simply add, nothing drops out. so you have to arrange it so that one of the variables will go away when you add

38. anonymous

ok when it comes to my problem i get really lost

39. anonymous

so for example if i see $2x+3y=7$ $x-y=1$ have to get rid of one variable by multiplying one equation all the way across by a number that will make one of the variables go away when i add

40. anonymous

so i could multiply the second equation by 3 and get $2x+3y=7$ $3x-3y=3$ and now it is easy add to get $5x=10$ so $x=2$

41. anonymous

in your problem you have $x-2y=12$ $11x+3y=-105.5$

42. anonymous

to make one of the variables go, multiply the top one by -11 so you will have $-11x$ in the first equation and $11x$ in the second one, and they will add up to zero

43. anonymous

we have to multiply EVERYTHING by -11 in the first equation and we get $-11x+22y=-132$ $11x+3y=-105.5$

44. anonymous

now when you add there will be no more x's

45. anonymous

ok is that the first part or the second part

46. anonymous

i am not sure what you mean

47. anonymous

step one was to turn $4x-8y=48$ into $x-2y=4$

48. anonymous

step two was to multiply by -11 to get $-11x+22y=-132$

49. anonymous

step 3 is to add it to the second equation. the x's add to zero and you get $25y=-137.5$

50. anonymous

step 4 is to solve for y via $y=-237.5\div 25$ $y=-9.5$

51. anonymous

typo in step 3, should have been $25y=-237.5$

52. anonymous

and finally to find x, replace y by -9.5 in either equation

53. anonymous

ok with x would you divide by 2 for the first step as well

54. anonymous

$x-2y=12$ $x-2\times (-9.5)=12$ $x+19=12$ $x=12-19$ $x=-7$

55. anonymous

you can divide the first equation by 4, because each term has a common factor of 4 just makes it easier to work with

56. anonymous

in general no, you do not divide as a first step. in general you see what you can multiply one equation by to make one variable drop out when you add the two equations

57. anonymous

ok still a little lost but getting the hang of it