## NY,NY Group Title HELPPP ME STUDY! solve algebraically for a and b and check: 3a+5b=4 4a+3b=-2 one year ago one year ago

1. goformit100 Group Title

You can use Matrix method for solving these two equations simultaneously

2. NY,NY Group Title

i only know substitution, graphing, and elimination method and those are the only methods i can use.

3. darkprince14 Group Title

try eliminating either a or b

4. darkprince14 Group Title

If you're looking for the point of intersection or the solution to those two then that's helpful if not, sorry, i have no clue what to do next ..

5. NY,NY Group Title

i need to find the value of a and b, not find the solution. like get a or b by itself.

6. darkprince14 Group Title

how about let a = 0 or something like that...

7. NY,NY Group Title

not working :(

8. theEric Group Title

Here's the plan; try to "get a in terms of b" (or "b in terms of a"). Really, I mean try to solve for a, so that it equals something that involves b (or solve for b so that it equals something that involves a).

9. NY,NY Group Title

yeah, i know. but how do i do that?

10. theEric Group Title

You can look at either equation, and solve for either variable. It's up to you!

11. theEric Group Title

It's all fair game in this problem. So pick and equation and pick a variable to solve for!

12. NY,NY Group Title

ok, 3a+5b=4. let's solve for a.

13. theEric Group Title

Okay, you start! I'll watch.

14. theEric Group Title

Unless you want to workon it together now; we can do that.

15. theEric Group Title

work on*

16. NY,NY Group Title

yeah, let's work on it together.

17. theEric Group Title

Alright. When equations aren't too complex, a great starting point is getting the terms containing variable you're solving for, a, on the opposite side of all the other terms. So look at 3a+5b=4. Which term (containing a) do we want to it's own side?

18. NY,NY Group Title

3a.

19. NY,NY Group Title

3a= -5b+4

20. theEric Group Title

I agree! And it's with 5b, which we need to get rid of. And it appears you know how to do that! Good! So now a is still stuck with something; it's being multiplied by 3! So can you fix that, too?

21. NY,NY Group Title

$a= \frac{ 5b+4 }{ 3 }$

22. theEric Group Title

close! You forgot your sign of 5b! You had it right before! I'm guessing you were distracted by Open Study's fancy equation thing, but I don't know.

23. theEric Group Title

so a=(-5b+4)/3

24. NY,NY Group Title

oopssss. i meant -5b*

25. NY,NY Group Title

yeahh

26. theEric Group Title

$a=\frac{-5b+4}{3}$Haha, that's fine! So we solved for a in that one equation, 3a+5b=4. a is always a is always (-5b+4)/3. So we can substitute it into another a's place. Try it in the other equation, 4a+3b=-2. the a will be replaced and the only variable in the equation will be b. The we can solve for b!

27. theEric Group Title

So, start by substitution!

28. NY,NY Group Title

-20b+16/3+3b=-2

29. theEric Group Title

Make sure you type (-20b+16)/3 + 3b = -2 ! I see you factored correctly, but the way you wrote it it didn't look like it was all divided by 3, though it really was! :)

30. theEric Group Title

So$\frac{-20b+16}{3}+3b = -2$

31. NY,NY Group Title

multiply by 3?

32. theEric Group Title

Yeah, I'd do that!

33. theEric Group Title

Just so that left-most b isn't divided by it.

34. NY,NY Group Title

-20b+16+3b=-6?

35. theEric Group Title

So$3(\frac{-20b+16}{3}+3b)=3(-2)$

36. theEric Group Title

Common mistake! Don't worry! You just have to remember to multiply each entire side by 3. That way you're doing the same thing to each side, so that the two new sides will still be equal.

37. NY,NY Group Title

i multiplied by 3 to -20b + 16 so that canceled the 3 out, and then i multiplied the -2 by 3, giving -6. what i do wrong?

38. theEric Group Title

You have to multiply 3b by 3 as well!

39. theEric Group Title

it becomes 9b!

40. theEric Group Title

So -20b+16+9b=-6 :)

41. theEric Group Title

I'm sure you'll see it soon.

42. NY,NY Group Title

ohhh. wow, yeah. b=2?

43. theEric Group Title

-20b+16+9b=-6 -20b+9b=-22 -11b=-22 22=11b 22/11=b 2=b Yeah!

44. theEric Group Title

I had to work it out to check, but we got the same thing.

45. NY,NY Group Title

yay :D thanks eric :D yur awesome :D

46. theEric Group Title

Sorry for the wait, Open Study glitched :P Recap, we solved for "a in terms of b" and we solved for b. Now we know b and can now solve for a!

47. theEric Group Title

My pleasure! Thank you for doing your part! You did great!

48. theEric Group Title

$a=\frac{-5b+4}{3}=\frac{-5(2)+4}{3}$ and compute... finale!

49. NY,NY Group Title

thanks :D

50. NY,NY Group Title

i just hope i do good on the quiz tomorrow...

51. NY,NY Group Title

a=-10+4/3 a=-6/3 a=-2

52. theEric Group Title

My pleasure. Did you get a = 2?

53. theEric Group Title

Best of luck! Tag me in any other questions you have, or you can ask them here. But the most important thing in these an dmany other math problems is planning! Knowing what you will do. This technique we used is good for this situation.

54. theEric Group Title

Haha!! Caught me! -2 ! :D

55. theEric Group Title

Serves me right for trying to do it in my head.

56. theEric Group Title

My responses are out of order. Open Stud is scrambled, it seems.

57. NY,NY Group Title

yeah. open study is being really laggy today. if i can just finish up my science homework, ill bring up some more questions to study with. thanks again :D and bye for now.

58. theEric Group Title

I'm glad it's not just me! No problem. Good luck with everything!