## anonymous one year ago Solve the following system of equations: x − 2y = 6 2x − 4y = 10

1. anonymous

do you move the x to the other side first or do you just solve

2. karatechopper

Well have you heard of substitution or elimination?

3. anonymous

yes

4. karatechopper

Which process do you prefer?

5. anonymous

substitution

6. anonymous

so the equation would look like this 2y=x-6

7. karatechopper

What variable do you want to use?

8. anonymous

x and y

9. karatechopper

Okay pick one. :)

10. anonymous

x-2y=6

11. karatechopper

Lol tyler. I'm asking you to pick a variable that we can solve for in order to substitute.

12. anonymous

oh lol x

13. karatechopper

ahah alrighty then.

14. karatechopper

x − 2y = 6 Solve that equation for x now. :)

15. anonymous

so you would substitute 0 for x and the equation (0)-2y=6

16. karatechopper

nooooooooooooo

17. karatechopper

where have you go that my friend

18. karatechopper

Solve for x :)

19. anonymous

oops

20. anonymous

x-2(0)=6

21. anonymous

x=6

22. karatechopper

.uhm. We need to isolate x x − 2y = 6 Add 2y to both sides in order to make x be on its own. Whats x= now?

23. anonymous

x=2y+6

24. karatechopper

YAY! :D

25. karatechopper

Okay now let's look at the second equation.

26. karatechopper

2x − 4y = 10

27. anonymous

ok

28. karatechopper

We know that x=2y+6 Now plug that value for x into this equation 2x − 4y = 10

29. anonymous

ok so 2(2y+6)-4y=10

30. anonymous

4y+12-4y=10

31. anonymous

8y+12=10 8y=-2

32. karatechopper

Wait a minute..

33. karatechopper

2(2y+6)-4y=10 4y+12-4y=10 4y-4y=0 12=10 Dang we did something wrong.

34. anonymous

yeah maybe we entered the wrong equation

35. karatechopper

uhm lets try solving for x in the bottom equation? 2x-4y=10

36. karatechopper

actually don't...it won't work again.

37. karatechopper

Are you okay if we try elimination?

38. anonymous

yeah sure

39. karatechopper

Yay. x − 2y = 6 2x − 4y = 10 Okay so let's try to eliminate x, we will multiply the top equation by -2, Could you do that for me please?

40. anonymous

yay

41. anonymous

you multiply everthing by two or what

42. karatechopper

yes by -2

43. anonymous

ok so -2x-(-4)y=-20

44. karatechopper

what is 6 x -2?

45. karatechopper

We just wanted to multiply x-2y=6 You should have gotten (-2)x-(-2)(2)y=6(-2)

46. anonymous

-2x-(-4)y=-12

47. karatechopper

okay what is a negative times a negative

48. anonymous

positive

49. anonymous

so its a positive 4y

50. karatechopper

yes

51. karatechopper

now rewrite the equation we have.

52. anonymous

-2x+4y=-12

53. karatechopper

Alright turn up.

54. anonymous

yay

55. karatechopper

So lets rewrite the whole thing. -2x+4y=-12 2x − 4y = 10 Now, solve it out. As you can see...both variables cancel out... Did you post the right question? Also, the answer because we cannot solve it is.... No solution.

56. anonymous

? Show that the solution to the system of equations 10x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 10x − 2y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 11x − y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 11x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

57. karatechopper

Woah there amigo, what is this?

58. anonymous

59. karatechopper

What? Those look like dif questions, I am confused.

60. anonymous

ok look at this

61. anonymous

A system of equations is shown below: 6x − 2y = 3 (equation 1) 5x + 3y = 4 (equation 2) A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof? Show that the solution to the system of equations 10x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 10x − 2y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 11x − y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 11x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

62. anonymous

thats the whole question

63. karatechopper

@TheSmartOne Will try to help you for a bit, I've got to finish something else. Hope I was some sort of help. Sorry.

64. anonymous

your fine you were help @karatechopper

65. TheSmartOne

which question are we working on?

66. anonymous

the one up above

67. anonymous

but ill show you it just in case you didnt see it

68. anonymous

A system of equations is shown below: 6x − 2y = 3 (equation 1) 5x + 3y = 4 (equation 2) A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof? Show that the solution to the system of equations 10x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 10x − 2y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 11x − y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations 11x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

69. TheSmartOne

It's an interesting problem, hmmmm.

70. TheSmartOne

can you add these 2 equations and tell me what you get: 6x − 2y = 3 5x + 3y = 4

71. anonymous

ok

72. TheSmartOne

so basically, what is 6x + 5x -2y + 3y = 3 + 4

73. anonymous

yeah sorry i was doing something else

74. anonymous

11x-y=7

75. TheSmartOne

and which answer choice has 11x-y=7 ?

76. anonymous

the third and the fourth one

77. anonymous

C and D

78. TheSmartOne

C has 11x $$\bf\color{red}{−}$$ y = 7 D has 11x $$\bf \color{red}{+}$$ y = 7

79. anonymous

80. anonymous

@TheSmartOne

81. TheSmartOne

correct

82. anonymous

awesome thank you

83. TheSmartOne

np :)