## anonymous 4 years ago Solve using the substitution method. 5x − 7y = −16, 2x + 8y = 26

1. Mertsj

Divide the second equation by 2 and solve it for x You will get x=13-4y Put that into the first equation in place ofx

2. anonymous

i would use the 2nd equation to substitute because the numbers are more simple. get down to x =( ) so 2x +8y = 26 2x = 26 -8y x = (26 - 8y)/2 x = 13 -4y now you can replace this x into the other equation 5x - 7y = -16 replace the x 5(13 - 4y) - 7y = -16 65 - 20y - 7y = -16 solve for y -27y = -71 y = 3 replace y=3 into any equation to find x 2x + 8y = 26 2x + 8(3) = 26 2x + 24 = 26 2x = 2 x =1 y = 3

3. anonymous

Ok mertsj I am still confused

4. Mertsj

Can you divide the second equation by 2?

5. Mertsj

|dw:1327112923657:dw|

6. anonymous

Ok I got that part

7. Mertsj

Now subtract 4y from both sides.

8. anonymous

so 4y-y7 and 13-4y

9. Mertsj

|dw:1327113113852:dw|

10. Mertsj

So do you know how to substitute that in the other equation?

11. anonymous

somewhat

12. Mertsj

Do you play a sport?

13. Mertsj

A team sport?

14. anonymous

no

15. Mertsj

Do you watch sports on tv?

16. anonymous

no sorry

17. Mertsj

Well I thought you might know what it means when the coach substitutes one player for another. Any way, we have to take that name for x that we just found and replace x with it.

18. anonymous

would you divide the other side by 2 as weel

19. anonymous

well*

20. Mertsj

|dw:1327113311498:dw|

21. Mertsj

Do you understand what I just did?

22. anonymous

somewhat

23. Mertsj

Now use the distributive property and collect like terms

24. anonymous

now math is my worst subject how do you do that

25. Mertsj

5(13-4y)=65-20y

26. Mertsj

Do you get that?

27. anonymous

now how did you get that

28. Mertsj

The 5 outside the parentheses means to multiply everything in the parentheses by 5.

29. anonymous

ok

30. Mertsj

So I multiplied 5 by 13 and got 65. Then I multiplied -4y by 5 and got -20y

31. Mertsj

Now -20y and -7y are like terms and they should be combined.

32. anonymous

ok got that

33. anonymous

so would it be 27y

34. Mertsj

Now subtract 65 from both sides.

35. Mertsj

It's actually -27y

36. Mertsj

|dw:1327113544265:dw|

37. anonymous

ok got that part

38. Mertsj

Now divide both sides by -27

39. anonymous

so would it be -27y/-27y and -16/-27y

40. Mertsj

|dw:1327113866037:dw|

41. Mertsj

Did you subtract 65 from BOTH SIDES?

42. anonymous

yes I did than what do I do

43. Mertsj

So what do you have now? Then I can tell you what to do next.

44. anonymous

this is all I have down

45. Mertsj

Do you have -27y=-81 ?

46. anonymous

5x − 7y = −16 5(13-4y)-7y=-16 5(13-4y)=65-20y 65-20y-7y=-16 -20y+-7y=-27y 65-27y=-16 -65 -65 ----------- -27y/-27y=-81/-27 y=3 2x/2 + 8y/2 = 2b/2 x + 4y = 13 -4y -4y x=13-4y

47. Mertsj

So yes. y=3.

48. Mertsj

x=13-4y so replace y with 3 and find x

49. Mertsj

x=13-4(3) x=13-12 x=1

50. anonymous

ok and that how both of them end

51. Mertsj

-27y/-27y=-81/-27 That is a step you did. You should have divided by -27 and NOT by y just -27

52. anonymous

oh ok

53. Mertsj

So yes. The solution is x = 1 and y = 3 which is the ordered pair (1,3) And if you would graph those equations, the two lines would cross at the point (1,3)

54. anonymous

ok but its just says solve so I don't have to graph it right

55. Mertsj

That's right. You don't have to graph it. I just wanted you to know the connection between the solution of the system and the graph.

56. anonymous

oh ok great thank you so much you really helped

57. Mertsj

yw

58. anonymous

have a good night

59. Mertsj

You too.