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anonymous

  • one year ago

PLZ HELP Equation A: y = x + 1 Equation B: y = 4x + 5 Which of the following steps can be used to find the solution to the set of equations? x + 1 = 4x + 5 x = 4x + 5 x + 1 = 4x x + 5 = 4x + 1

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  1. anonymous
    • one year ago
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    @JoannaBlackwelder

  2. JoannaBlackwelder
    • one year ago
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    Any thoughts?

  3. anonymous
    • one year ago
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    not really I'm so confused

  4. JoannaBlackwelder
    • one year ago
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    Ok, they are using the method of substitution.

  5. anonymous
    • one year ago
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    ok

  6. JoannaBlackwelder
    • one year ago
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    That is where you solve for a variable and plug it into that variable in the other equation.

  7. JoannaBlackwelder
    • one year ago
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    Both of these equations are already solved for y.

  8. JoannaBlackwelder
    • one year ago
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    So, we can take what y= in one equation, and plug it in for y in the other equation.

  9. JoannaBlackwelder
    • one year ago
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    |dw:1440003635482:dw|

  10. anonymous
    • one year ago
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    i thought y = 4x

  11. JoannaBlackwelder
    • one year ago
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    I'm not sure what you mean.

  12. anonymous
    • one year ago
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    in equation b

  13. anonymous
    • one year ago
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    or is that just the slope formula

  14. JoannaBlackwelder
    • one year ago
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    Equation b is close to the slope formula, y=mx+b, but it has an x instead of y.

  15. anonymous
    • one year ago
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    ok

  16. JoannaBlackwelder
    • one year ago
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    But have you followed what I have said so far?

  17. anonymous
    • one year ago
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    yes

  18. JoannaBlackwelder
    • one year ago
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    So, if you plug in x+1 for y in the second equation, what do you get?

  19. anonymous
    • one year ago
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    y=4x+6?

  20. JoannaBlackwelder
    • one year ago
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    Hm, no, if we are subbing x+1 in for y, then we don't have y anymore.|dw:1440004062537:dw|

  21. anonymous
    • one year ago
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    oh

  22. JoannaBlackwelder
    • one year ago
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    :-) Does that make sense?

  23. anonymous
    • one year ago
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    yep

  24. JoannaBlackwelder
    • one year ago
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    Cool, so what is the answer?

  25. anonymous
    • one year ago
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    a

  26. JoannaBlackwelder
    • one year ago
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    Yep!

  27. anonymous
    • one year ago
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    can u do another plz?

  28. anonymous
    • one year ago
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    ;)

  29. JoannaBlackwelder
    • one year ago
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    Sure

  30. anonymous
    • one year ago
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    Equation C: y = 6x + 9 Equation D: y = 6x + 2 Which of the following options is true about the solution to the given set of equations? One solution No solution Two solutions Infinite solutions

  31. JoannaBlackwelder
    • one year ago
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    Ok, well, let's see what happens if we do the same thing as the last problem.

  32. JoannaBlackwelder
    • one year ago
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    What do you get when you sub 6x+9 for y in the second equation?

  33. anonymous
    • one year ago
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    6x+9=6x+2?

  34. JoannaBlackwelder
    • one year ago
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    Sweet! Can you simplify that?

  35. anonymous
    • one year ago
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    combine like terms?

  36. JoannaBlackwelder
    • one year ago
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    Yep

  37. anonymous
    • one year ago
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    12x+9=+2??

  38. anonymous
    • one year ago
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    @JoannaBlackwelder

  39. JoannaBlackwelder
    • one year ago
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    No, to move one 6x to the other side, we need to subtract it

  40. JoannaBlackwelder
    • one year ago
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    |dw:1440004496684:dw|

  41. anonymous
    • one year ago
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    ohhhh i get it

  42. anonymous
    • one year ago
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    so theres only one solution?

  43. JoannaBlackwelder
    • one year ago
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    Sweet! So, any thoughts of what that tells us?

  44. JoannaBlackwelder
    • one year ago
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    Hm, no. When the two equations simplify to a false statement (9 does not equal 2),

  45. JoannaBlackwelder
    • one year ago
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    That means no solution

  46. anonymous
    • one year ago
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    ohh

  47. JoannaBlackwelder
    • one year ago
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    We can graph them to show that too.

  48. JoannaBlackwelder
    • one year ago
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    They have the same slope, but different y intercepts

  49. JoannaBlackwelder
    • one year ago
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    So they are parallel lines, and will never cross.

  50. JoannaBlackwelder
    • one year ago
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    The solution is the point where the two lines cross.

  51. anonymous
    • one year ago
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    one more??

  52. JoannaBlackwelder
    • one year ago
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    Sure :-)

  53. anonymous
    • one year ago
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    y = 3x + 4 2x + 3y = 10 Which of the following steps could be used to solve by substitution? 3x + 4 = 2x + 3y 2x + 3(3x + 4) = 10 2(3x + 4) + 3y = 10 3(y = 3x + 4)

  54. JoannaBlackwelder
    • one year ago
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    Ok, any thoughts?

  55. anonymous
    • one year ago
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    no

  56. JoannaBlackwelder
    • one year ago
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    The first equation is solved for y.

  57. JoannaBlackwelder
    • one year ago
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    So, we take what y is in terms of x, and plug it into the other equation.

  58. JoannaBlackwelder
    • one year ago
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    Can you try to do that?

  59. anonymous
    • one year ago
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    im lost, ugh and my online teacher keeps reminding me about time crunch lol

  60. JoannaBlackwelder
    • one year ago
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    |dw:1440004939079:dw| Aw, that's frustrating!

  61. anonymous
    • one year ago
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    i see

  62. JoannaBlackwelder
    • one year ago
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    It is like the other ones, just the second equation isn't solved for y.

  63. anonymous
    • one year ago
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    ho do i slove

  64. anonymous
    • one year ago
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    how

  65. JoannaBlackwelder
    • one year ago
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    We aren't supposed to solve, just substitute.

  66. anonymous
    • one year ago
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    ok

  67. JoannaBlackwelder
    • one year ago
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    |dw:1440005055460:dw|

  68. JoannaBlackwelder
    • one year ago
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    See how I subbed the 3x+4 in for y in the second equation?

  69. anonymous
    • one year ago
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    yes

  70. JoannaBlackwelder
    • one year ago
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    That is all we have to do :-)

  71. JoannaBlackwelder
    • one year ago
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    Which answer does that look like?

  72. anonymous
    • one year ago
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    b

  73. JoannaBlackwelder
    • one year ago
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    Right

  74. anonymous
    • one year ago
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    one more, last one i promise lol

  75. JoannaBlackwelder
    • one year ago
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    Haha, ok

  76. anonymous
    • one year ago
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    d + e = 15 −d + e = −5 Label the ordered pair as (d, e). (0, 0) (10, −5) (5, 10) (10, 5)

  77. JoannaBlackwelder
    • one year ago
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    Ok, this one we actually do have to solve. Any thoughts on how to start?

  78. anonymous
    • one year ago
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    not really

  79. JoannaBlackwelder
    • one year ago
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    Well, what happens when we add the two equations together?

  80. anonymous
    • one year ago
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    we sub?

  81. JoannaBlackwelder
    • one year ago
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    We could, but we would have to solve for one of the variables first.

  82. anonymous
    • one year ago
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    ok

  83. JoannaBlackwelder
    • one year ago
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    I would suggest to use elimination on this one. It is the easier method. :-)

  84. anonymous
    • one year ago
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    ok

  85. JoannaBlackwelder
    • one year ago
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    |dw:1440005374033:dw| What happens when we add the two equations together?

  86. anonymous
    • one year ago
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    im not sure

  87. JoannaBlackwelder
    • one year ago
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    Just take a guess

  88. anonymous
    • one year ago
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    elimintion

  89. JoannaBlackwelder
    • one year ago
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    Ok, but what equation are we left with?

  90. anonymous
    • one year ago
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    i honestly don't know

  91. JoannaBlackwelder
    • one year ago
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    |dw:1440005536799:dw| See how I added the equations together?

  92. anonymous
    • one year ago
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    yes

  93. JoannaBlackwelder
    • one year ago
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    Can you combine like terms?

  94. anonymous
    • one year ago
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    ill be back in one min, my teacher is calling me

  95. JoannaBlackwelder
    • one year ago
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    Ok

  96. anonymous
    • one year ago
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    I'm back @JoannaBlackwelder

  97. JoannaBlackwelder
    • one year ago
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    Ok, can you combine like terms?

  98. anonymous
    • one year ago
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    that one is kinda hard

  99. JoannaBlackwelder
    • one year ago
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    It is a little different. d-d is what?

  100. anonymous
    • one year ago
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    d

  101. JoannaBlackwelder
    • one year ago
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    No, it is like 2-2.

  102. anonymous
    • one year ago
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    0

  103. JoannaBlackwelder
    • one year ago
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    Right. :-)

  104. JoannaBlackwelder
    • one year ago
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    And e+e is what?

  105. anonymous
    • one year ago
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    e

  106. JoannaBlackwelder
    • one year ago
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    No, we add the coefficients, and when there is no coefficient written it is understood to be 1. So this is 1e+1e

  107. anonymous
    • one year ago
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    2

  108. JoannaBlackwelder
    • one year ago
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    Close, 2e

  109. anonymous
    • one year ago
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    oh i see

  110. JoannaBlackwelder
    • one year ago
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    :-) And what is 15-5?

  111. anonymous
    • one year ago
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    10

  112. JoannaBlackwelder
    • one year ago
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    |dw:1440006758146:dw| Great!

  113. JoannaBlackwelder
    • one year ago
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    See how I simplified that?

  114. anonymous
    • one year ago
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    yep

  115. JoannaBlackwelder
    • one year ago
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    Sweet, so we need to finish getting e by itself.

  116. JoannaBlackwelder
    • one year ago
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    It is currently multiplied by 2

  117. JoannaBlackwelder
    • one year ago
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    So, we need to divide the left side by 2 to leave just e (or 1e)

  118. anonymous
    • one year ago
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    |dw:1440006877761:dw|

  119. JoannaBlackwelder
    • one year ago
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    Good effort! But we need to divide by 2 to get e by itself, not 10

  120. anonymous
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    ok

  121. JoannaBlackwelder
    • one year ago
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    |dw:1440006917075:dw|

  122. anonymous
    • one year ago
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    ok

  123. anonymous
    • one year ago
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    so whats my second point

  124. JoannaBlackwelder
    • one year ago
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    Well, now that we know that e is 5, which answers do we have to choose from?

  125. anonymous
    • one year ago
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    c,d

  126. anonymous
    • one year ago
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    ?

  127. JoannaBlackwelder
    • one year ago
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    Are you sure that both c and d have e being 5?

  128. anonymous
    • one year ago
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    c?

  129. JoannaBlackwelder
    • one year ago
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    No, c, has e as 10.

  130. anonymous
    • one year ago
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    d

  131. JoannaBlackwelder
    • one year ago
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    Yep, that is the only answer that has e as 5. We would normally also have to find d, but they gave us a shortcut. :-)

  132. anonymous
    • one year ago
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    thank u

  133. JoannaBlackwelder
    • one year ago
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    You're welcome

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