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Math Help - Alegebra Equations

  1. #1
    Member Rimas's Avatar
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    Alegebra Equations

    Given the equation 3x+y=17 5y+z=14 and 3x+5z=41 what is the value if the sum x+y+z
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  2. #2
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    Quote Originally Posted by Rimas View Post
    Given the equation 3x+y=17 5y+z=14 and 3x+5z=41 what is the value if the sum x+y+z
    Hello,

    you've got a system of 3 simultaneously equations:

    \begin {array}{l}3x+y\ \ =17 \\\ \ \ \ 5y+z=14 \\ 3x\ \ \ \  +5z=41 \end {array}

    I don't know which method you use to solve this system of equations. I solved the EQU1 for y and plugged this term into EQU2. I got:

    3x + 5z = 41
    -15x + z = -71

    Multiply the 1rst equation by 5 and add:

    26z = 134. Solve for z. Re-substitute this value and solve for x. Re-substitute the value of z in the EQU2 and solve for y.

    You'll get:
    x=\frac{66}{13}\ \wedge \ y=\frac{23}{13}\ \wedge \ z=\frac{67}{13}

    The sum of these three numbers is 12

    EB
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Rimas View Post
    Given the equation 3x+y=17 5y+z=14 and 3x+5z=41 what is the value if the sum x+y+z
    Add the equations together:

    (3x+y) + (5y+z) + (3x+5z) = 17 + 14 + 41

    this simplifies to:

    6x + 6y + 6z = 72,

    divide by 6:

    x + y + z = 12.

    RonL
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