How do you solve the system $w + 4 x + 3 y - 11 z = 42$ $w+4x+3y-11z=42$ , $6 w + 9 x + 8 y - 9 z = 31$ $6w+9x+8y-9z=31$ and $- 5 w + 6 x + 3 y + 13 z = 2$ $-5w+6x+3y+13z=2$ , $8 w + 3 x - 7 y + 6 z = 31$ $8w+3x-7y+6z=31$ ?

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How do you solve the system $w + 4 x + 3 y - 11 z = 42$ $w+4x+3y-11z=42$ , $6 w + 9 x + 8 y - 9 z = 31$ $6w+9x+8y-9z=31$ and $- 5 w + 6 x + 3 y + 13 z = 2$ $-5w+6x+3y+13z=2$ , $8 w + 3 x - 7 y + 6 z = 31$ $8w+3x-7y+6z=31$ ?

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Answer 1 · 2016-02-20T23:18:37

$((w),(x),(y),(z)) = ((-12054/4889),(38342/4889),(-31301/4889),(-14357/4889))$

Explanation:

Rewrite the equation in linear vector and matrix form:
$((1,4,3,-11), (6,9,8,-9), (-5,6,3,13 ), (8,3,-7,6 )) ((w ),(x ), (y ), (z ))= ((42 ),(31 ), (2 ), (31 ))$
Now use gauss elimination to solve the matrix equation. THe goal here is the convert the 4x4 matrix in half diagonal matrix and solve back from the half diagonal... Used a calculator on Matrix mode to solve:
$((w),(x),(y),(z)) = ((-12054/4889),(38342/4889),(-31301/4889),(-14357/4889))$

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How do you solve the system $w + 4 x + 3 y - 11 z = 42$ $w+4x+3y-11z=42$ , $6 w + 9 x + 8 y - 9 z = 31$ $6w+9x+8y-9z=31$ and $- 5 w + 6 x + 3 y + 13 z = 2$ $-5w+6x+3y+13z=2$ , $8 w + 3 x - 7 y + 6 z = 31$ $8w+3x-7y+6z=31$ ?

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Explanation:

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How do you solve the system w+4x+3y-11z=42w+4x+3y−11z=42w+4x+3y-11z=42 , 6w+9x+8y-9z=316w+9x+8y−9z=316w+9x+8y-9z=31 and -5w+6x+3y+13z=2−5w+6x+3y+13z=2-5w+6x+3y+13z=2, 8w+3x-7y+6z=318w+3x−7y+6z=318w+3x-7y+6z=31?

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Explanation:

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How do you solve the system $w + 4 x + 3 y - 11 z = 42$ $w+4x+3y-11z=42$ , $6 w + 9 x + 8 y - 9 z = 31$ $6w+9x+8y-9z=31$ and $- 5 w + 6 x + 3 y + 13 z = 2$ $-5w+6x+3y+13z=2$ , $8 w + 3 x - 7 y + 6 z = 31$ $8w+3x-7y+6z=31$ ?