MightySmurf 4 years ago Solve this system of equations using the addition method. 3x-y=9 2x+y=6 Solve this system of equations using the addition method. 3x-y=9 2x+y=6 @Mathematics

1. conheomap

5x + 0 = 15 x = 3 plug to the first equation 2.3 + y = 6 y = 0

2. MightySmurf

so i would just add the numbers then divide

3. conheomap

first add the equation 1 and 2 so that it will get rid of one of the variable In this example, you got it easy because in equation 1 you have -y, and in equation 2 you have y, so the sum of these equations will get rid of y

4. conheomap

in case you want to get rid of x first. then you would have to do the following: multiply 1st equation by 2 multiply 2nd equation by -3 so that it would appear like this 6x .... -6x ------------- 0x ......

5. MightySmurf

im sorry im very confused..see im takin algebra online and dnt have a teacher so i have to take tests online and have no idea how to do them

6. conheomap

ok so you have two equations and two variables which is x, y. They ask you to find those values of x, y so that when you plug them in to any equation, they have to be true. In this case if you plug x = 0 and y = 3. Both equations hold. That's how it goes anyways.

7. conheomap

Now they asked you to use addition method which means. some how you have to add equation 1 and equation 2

8. conheomap

3x-y=9 + 2x+y=6 ---------- 5x + 0 = 15 the new equation only has x now. So you know what x is, just plug into any of the equations they gave you, you will get y value.

9. conheomap

give me another problem, i'll explain in more details because this is problem is very simple.

10. MightySmurf

ok 4a-5b=7 4a+5b=17

11. conheomap

alright. this is also simple. Let's change to 4a + 5b = 7 2a + 3b = 9 instead.

12. conheomap

now what do you do? I want to know how you do it, then I'll explain

13. MightySmurf

i add 4a to 2a right

14. conheomap

continue

15. MightySmurf

16. conheomap

ok. but the new equation doesn't get rid of any variables right? so your stuck

17. conheomap

you have to modify the original equations somehow so when adding you will get either 0x or 0y

18. conheomap

look at this problem you gave me: 4a-5b=7 4a+5b=17 notice the -5b (1st) and 5b (2nd equation). when adding the result is 0b. that's why i said they gave you a simple problem. Just adding.

19. conheomap

did you learn how to modify the equations yet? or just purely adding stuff?

20. MightySmurf

no did learn to modify the equations

21. conheomap

okay then please try to modify this one: 4a + 5b = 7 2a + 3b = 9

22. MightySmurf

i cnt i dnt understand how to modify im sorry

23. conheomap

let's try to modify so when adding I will get 0a ok?

24. conheomap

i see first equation have 4a. the 2nd have 2a. ... I need to have some how to have 2nd equation to have -4a. Right?

25. MightySmurf

ummm yes

26. conheomap

you can do this by multiply 2nd equation by -2

27. conheomap

what's the modified equation now?

28. conheomap

ok the modified (2nd equation) becomes: -4a -6b = -18

29. conheomap

now you can add the first and the modified.

30. MightySmurf

so then id add the 4a and 5b

31. conheomap

no no. it's gonna be like this: 4a + 5b = 7 + -4a -6b = -18 ----------------------- 0a -b = -11

32. conheomap

you only add the a and a... b and b not a and b.

33. MightySmurf

o

34. conheomap

so now you can solve for the b value. Once you have one variable solved, plug to any of the original equation, then bam. That's it

35. conheomap

can you modify to get rid of b instead of a this time? it's a bit harder, but same method. 4a + 5b = 7 2a + 3b = 9

36. conheomap

you have to modify both equations for b.

37. MightySmurf

4a+2a right

38. conheomap

39. MightySmurf

5b+3b?

40. conheomap

so you will get 6a + 8b = 16?

41. conheomap

it doesn't get rid of b does it?

42. MightySmurf

so i subtract

43. conheomap

you need to get help from professor about this. But those problems you gave me. you can just add them directly without modifying anything.

44. conheomap

45. conheomap

one thing I can tell you that when adding you must get rid of one of the variables.

46. MightySmurf

no im not im sorry thnks for tryin to help tho

47. conheomap

i have to go home. sorry

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