How do you solve using gaussian elimination or gauss-jordan elimination, $6 x + 2 y + 7 z = 20$ $6x+2y+7z=20$ , $- 4 x + 2 y + 3 z = 15$ $-4x+2y+3z=15$ , $7 x - 3 y + z = 25$ $7x-3y+z=25$ ?

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How do you solve using gaussian elimination or gauss-jordan elimination, $6 x + 2 y + 7 z = 20$ $6x+2y+7z=20$ , $- 4 x + 2 y + 3 z = 15$ $-4x+2y+3z=15$ , $7 x - 3 y + z = 25$ $7x-3y+z=25$ ?

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Answer 1 · 2016-01-26T14:34:42

$x = \frac{325}{102}$ $x = 325/102$

$y = - \frac{165495}{2601}$ $y= -165495/2601$

$z = \frac{470}{51}$ $z = 470/51$

Explanation:

$6 x + 2 y + 7 z = 20$ $6x+2y+7z = 20$
$- 4 x + 2 y + 3 z = 15$ $-4x +2y +3z = 15$
$7 x - 3 y + z = 25$ $7x - 3y +z = 25$

Gaussian elimination is a process of solving simultaneous equations in more than two variables by repeatedly adding and/or subtracting the equations.
Observing that there is an element $+ 2 y$ $+2y$ in each of the first two equations, if we subtract the middle equation from the first one we get
$10 x + 4 z = 5$ $10x+4z = 5$

If we add $3 \cdot$ $3*$ the second equation to $2 \cdot$ $2*$ the third equation

$- 12 x + 6 y + 9 z = 45$ $-12x+6y+9z=45$
$14 x - 6 y + 2 z = 50$ $14x-6y+2z=50$

we get $2 x + 11 z = 95$ $2x+11z = 95$

Using a similar process on these two equations in $x$ $x$ and $z$ $z$
$10 x + 4 z = 5$ $10x+4z = 5$
$10 x + 55 z = 475$ $10x+55z = 475$
$51 z = 470$ $51z = 470$

$z = \frac{470}{51}$ $z = 470/51$

$x = \frac{5 - 4 z}{10} = \frac{255 - 1880}{510} = \frac{1625}{510} = \frac{325}{102}$ $x = (5-4z)/10 = (255 - 1880)/510 =1625/510 = 325/102$

Select any one of the original equations to solve for $y$ $y$

$2 y = 20 - 6 \cdot (\frac{325}{102}) - 7 \cdot (\frac{470}{51})$ $2y = 20 -6*(325/102) - 7*(470/51)$
$2 y = \frac{20 \cdot 102 \cdot 51 - 6 \cdot 325 \cdot 51 - 7 \cdot 102 \cdot 470}{102 \cdot 51}$ $2y = (20*102*51 - 6*325*51 - 7*102*470)/(102*51)$

$y = \frac{104040 - 99450 - 335580}{5202}$ $y = (104040 - 99450 -335580)/5202$
$y = - \frac{330990}{5202} = - \frac{165495}{2601}$ $y= - 330990/5202 = -165495/2601$

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How do you solve using gaussian elimination or gauss-jordan elimination, $6 x + 2 y + 7 z = 20$ $6x+2y+7z=20$ , $- 4 x + 2 y + 3 z = 15$ $-4x+2y+3z=15$ , $7 x - 3 y + z = 25$ $7x-3y+z=25$ ?

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How do you solve using gaussian elimination or gauss-jordan elimination, 6x+2y+7z=206x+2y+7z=20, −4x+2y+3z=15-4x+2y+3z=15, 7x−3y+z=257x-3y+z=25?

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Explanation:

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How do you solve using gaussian elimination or gauss-jordan elimination, $6 x + 2 y + 7 z = 20$ $6x+2y+7z=20$ , $- 4 x + 2 y + 3 z = 15$ $-4x+2y+3z=15$ , $7 x - 3 y + z = 25$ $7x-3y+z=25$ ?