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

1. goformit100

You can use Matrix method for solving these two equations simultaneously

2. NY,NY

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

3. darkprince14

try eliminating either a or b

4. darkprince14

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

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

6. darkprince14

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

7. NY,NY

not working :(

8. theEric

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

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

10. theEric

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

11. theEric

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

12. NY,NY

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

13. theEric

Okay, you start! I'll watch.

14. theEric

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

15. theEric

work on*

16. NY,NY

yeah, let's work on it together.

17. theEric

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

3a.

19. NY,NY

3a= -5b+4

20. theEric

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

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

22. theEric

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

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

24. NY,NY

oopssss. i meant -5b*

25. NY,NY

yeahh

26. theEric

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

So, start by substitution!

28. NY,NY

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

29. theEric

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

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

31. NY,NY

multiply by 3?

32. theEric

Yeah, I'd do that!

33. theEric

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

34. NY,NY

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

35. theEric

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

36. theEric

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

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

You have to multiply 3b by 3 as well!

39. theEric

it becomes 9b!

40. theEric

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

41. theEric

I'm sure you'll see it soon.

42. NY,NY

ohhh. wow, yeah. b=2?

43. theEric

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

44. theEric

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

45. NY,NY

yay :D thanks eric :D yur awesome :D

46. theEric

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

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

48. theEric

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

49. NY,NY

thanks :D

50. NY,NY

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

51. NY,NY

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

52. theEric

My pleasure. Did you get a = 2?

53. theEric

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

Haha!! Caught me! -2 ! :D

55. theEric

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

56. theEric

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

57. NY,NY

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

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