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Math Help - Solving Using Substitution

  1. #1
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    Solving Using Substitution

    Hey Everyone! I'm going to have a few emergency help questions today and early tomorrow. I have a huge test.

    My problem right now is solving with substitution, and I am given the following problem to do so with:

    4x+y=5
    2x-3y=13

    I'm thinking I should bring up the 2x or the 3 from the bottom equation to the top? T

    Thanks!
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  2. #2
    Super Member Quacky's Avatar
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    Re: Solving Using Substitution

    Rearranging the first to isolate y:

    y=5-4x
    Now attempt to substitute this into the second equation. If you can't, then please show your working.
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  3. #3
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    Re: Solving Using Substitution

    Multiply the second equation through by 2 then subtract the result from the first equation.
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  4. #4
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    Re: Solving Using Substitution

    Hello, annon25!

    Solve by substitution: . \begin{array}{cccc}4x+y&=&5 & [1] \\ 2x-3y&=&13 & [2]\end{array}

    I'm thinking I should bring up the 2x or the 3 from the bottom equation to the top?
    What does that mean?

    Do you understand the substitution method?

    [1] Solve one of the equations for one of its variables.
    [2] Substitute this into the other equation and solve for the remaining variable.
    [3] Then solve for the other variable.

    Solve [1] for y\!:\;\;y \:=\:5-4x

    Substitute into [2]: . 2x - 3(5-4x) \:=\:13

    . . . . and we have: . 2x - 15 + 12x \:=\:13 \quad\Rightarrow\quad 14x \:=\:28 \quad\Rightarrow\quad x \,=\,2

    Substitute into [1]: . 4(2) + y \:=\:5 \quad\Rightarrow\quad y \,=\,\text{-}3


    Therefore: . \begin{Bmatrix}x &=& \;2 \\ y &=& \text{-}3 \end{Bmatrix}

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  5. #5
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    Re: Solving Using Substitution

    Quote Originally Posted by annon25 View Post
    Hey Everyone! I'm going to have a few emergency help questions today and early tomorrow. I have a huge test.

    My problem right now is solving with substitution, and I am given the following problem to do so with:

    4x+y=5
    2x-3y=13

    I'm thinking I should bring up the 2x or the 3 from the bottom equation to the top? T

    Thanks!
    Since the questions states substitution I would not use pickslide's methods (which is elimination). What it wants you to do is sub an expression for either x or y into the other equation solving for one of the variables then finding the other.

    In your case it is easier to subtract 4x from both sides to get y = 5-4x. You can now sub 5-4x for y in the second equation: 2x-3(5-4x) = 13.

    You can now find x and then use the first equation to find y
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  6. #6
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    Re: Solving Using Substitution

    Okay,
    This is what I ended up with:

    2x-4x-3y

    If I plug in 2 as x and-3 as y, I am getting the answer "5..."
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  7. #7
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    Re: Solving Using Substitution

    Quote Originally Posted by annon25 View Post
    Okay,
    This is what I ended up with:

    2x-4x-3y

    If I plug in 2 as x and-3 as y, I am getting the answer "5..."
    Soroban has answered your question.
    Last edited by mr fantastic; November 29th 2011 at 02:31 PM.
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