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Math Help - What is the intersection of the following lines...

  1. #1
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    What is the intersection of the following lines...

    y - 3x + 2 = 0

    and

    -3x + 4y -1 = 0

    Thanks!
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  2. #2
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    Quote Originally Posted by gobbajeezalus View Post
    y - 3x + 2 = 0

    y = 3x - 2

    and

    -3x + 4y -1 = 0

    4y = 3x + 1

    y = (3x + 1)/4

    Thanks!
    set the two expressions that equal y equal to each other. solve for x, then determine the value of y.
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  3. #3
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    Talking answer

    Quote Originally Posted by gobbajeezalus View Post
    y - 3x + 2 = 0

    and

    -3x + 4y -1 = 0

    Thanks!

    y-3x=-2
    4y-3x=1 (you change the signs on one of the lines and the x's go)

    -y+3x=2
    4y-3x=1

    3y=3 y=1

    now you fill in for y


    y-3x=-2

    (1)-3x=-2

    -3x=-3 -x=-1 x=1

    there for (1,1) are the points
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  4. #4
    Member TheMasterMind's Avatar
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    Quote Originally Posted by gobbajeezalus View Post
    y - 3x + 2 = 0

    and

    -3x + 4y -1 = 0

    Thanks!
    The easiest thing to do when to already have a variable isolated (in this case y) is to use the method of substitution

    (1) y-3x+2=0

    (2)-3x+4y-1=0

    Isolate y in the first equation

    y=3x-2

    Plug that value into the second equation and solve for x

    -3x+4(3x-2)-1=0

    <br />
-3x+12x-8-1=0

    9x=9

    x=1

    Plug that value of x into equation 1 and solve for y

    <br />
y-3(1)+2=0

    y-1=0

    y=1

    \therefore the intersection of the lines occurs at point (1,1)
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