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## Bieber896 one year ago can someone help me on substituting and eliminating systems of equations?! I'm so confused

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1. jim_thompson5910

Post the full problem please

2. Bieber896

x=3y-8 5y=19+4x

3. Bieber896

@jim_thompson5910

4. jim_thompson5910

since x is fully isolated, you can replace the x in the second equation with 3y-8 so 5y=19+4x turns into 5y=19+4(3y-8)

5. jim_thompson5910

do you see how to solve for y?

6. Bieber896

5y=19+12y-32??

7. Bieber896

but there's two ys

8. jim_thompson5910

get all the y terms to one side so subtract 12y from both sides to get the y terms to the left side

9. Bieber896

-7y=19+(-32)?

10. jim_thompson5910

good, then combine like terms on the right side

11. Bieber896

-7y=-13

12. jim_thompson5910

what comes next

13. Bieber896

divide both sides by -7?

14. jim_thompson5910

correct

15. jim_thompson5910

$\Large -7y = -13$ $\Large \frac{-7y}{-7} = \frac{-13}{-7}$ $\Large y = \frac{13}{7}$ Notice how the two negatives divide to make a positive result

16. Bieber896

so y=1.85

17. jim_thompson5910

I'd leave it as a fraction because the decimal result is only an approximation

18. Bieber896

oh ok

19. Bieber896

so then do I plug that in to the next equation?

20. jim_thompson5910

yes, you'll plug that into x=3y-8 to find x

21. Bieber896

so x=-2 3/7

22. jim_thompson5910

or x = -17/7 so the solution as an ordered pair is $$\LARGE \left( -\frac{17}{7}, \frac{13}{7}\right)$$

23. Bieber896

ok thanks so much ! can we just do one more?!

24. anonymous

yes

25. jim_thompson5910

sure

26. Bieber896

y=3x+3 y=2x+1

27. jim_thompson5910

y is equal to 3x+3 AND it's also equal to 2x+1

28. jim_thompson5910

since y is equal to those two things, we can set the two equal to each other basically we're performing a substitution

29. jim_thompson5910

y=2x+1 3x+3 = 2x+1 ... replace y with 2x+1 solve for x to get x = ??

30. Bieber896

so do I have to get rid of one of the variables?

31. anonymous

isolate your x

32. jim_thompson5910

move the 2x over you do this by subtracting 2x from both sides

33. anonymous

x=___

34. Bieber896

1x+3=+1

35. jim_thompson5910

now subtract 3 from both sides to move that 3 to the right side

36. Bieber896

1x=-2

37. jim_thompson5910

which is the same as x = -2

38. Bieber896

yup

39. Bieber896

then plug it in

40. jim_thompson5910

now plug that into either equation to find y

41. Bieber896

so the solution is (-2,3)

42. Bieber896

or -3 lol my bad

43. jim_thompson5910

yes it's (-2,-3)

44. Bieber896

thank you both so much for your help @jim_thompson5910 @tekman1298

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