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Thread: Systems of equations.

  1. #1
    Member MathBlaster47's Avatar
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    Systems of equations.

    Here is a problem I don't quite know what to do with.

    Solve the system of equations.
    $\displaystyle 3x+4y+z=7$
    $\displaystyle 2y+z=3$
    $\displaystyle -5x+3y+8z=-31$

    should I just solve for z by isolating it on one side of the equation like I would normally or is there a better method?
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  2. #2
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    Quote Originally Posted by MathBlaster47 View Post
    Here is a problem I don't quite know what to do with.

    Solve the system of equations.
    $\displaystyle 3x+4y+z=7$
    $\displaystyle 2y+z=3$
    $\displaystyle -5x+3y+8z=-31$

    should I just solve for z by isolating it on one side of the equation like I would normally or is there a better method?
    i would prefer the matrix method. X=A^(-1).B where X=(x,y,z),
    A=(3,4,1)
    (2,0,1)
    (-5,3,8)
    B=(7,3,-31) where A is a 3 by 3 matrix and X and B are 3 by 1 matrices.
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by MathBlaster47 View Post
    Here is a problem I don't quite know what to do with.

    Solve the system of equations.
    $\displaystyle 3x+4y+z=7$
    $\displaystyle 2y+z=3$
    $\displaystyle -5x+3y+8z=-31$

    should I just solve for z by isolating it on one side of the equation like I would normally or is there a better method?
    Hi MathBlaster47,

    There are several ways to solve a system like this, but your way seems to be a good start.

    (1) $\displaystyle 3x+4y+z=7$

    (2) $\displaystyle 2y+z=3$

    (3) $\displaystyle -5x+3y+8z=-31$

    Solve (2) for z: $\displaystyle z=3-2y$

    Substitute this for y in (1) and (3).

    (1) $\displaystyle 3x+4y+3-2y=7$

    (3) $\displaystyle -5x+3y+8(3-2y)=-31$

    Solve these two equations for x and y by using substitution or elimination method. Then, substitute your value for y into (2) to find z.

    (1) $\displaystyle 3x+2y=4$

    (3) $\displaystyle -5x-13y=-55$

    Multiply (1) by 5. Multiply (2) by 3.

    (1) $\displaystyle 15x+10y=20$

    (3) $\displaystyle -15x-39y=-165$

    Add (1) + (3).

    $\displaystyle -29y=-145$

    $\displaystyle \boxed{y=5}$

    I'll leave the rest for you. Good luck.
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