How do you solve using gaussian elimination or gauss-jordan elimination, $2 x - 3 y = 5$ $2x - 3y = 5$ , $3 x + 4 y = - 1$ $3x + 4y = -1$ ?

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Answer 1 · 2016-11-27T00:20:25

$x = 1, y = - 1$ $x=1, y=-1$

We can write the system of linear equation in matrix vector form

$A ulx = ulb$

$( (2,-3), (3,4) ) ( (x), (y) ) = ( (5), (-1) )$

So the Augmented Matrix is:

$( (2,-3,|,5), (3,4,|,-1) )$

$( (2,-3,|,5), (3,4,|,-1) ) stackrel(1/2R_1 rarr R_1)(rarr) ( (1,-3/2,|,5/2), (3,4,|,-1) )$

$( (1,-3/2,|,5/2), (3,4,|,-1) ) stackrel(R_2-3R_1 rarr R_2)(rarr) ( (1,-3/2,|,5/2), (0,17/2,|,-17/2) )$

And so:
$17/2y=-17/2 => y=-1$

Back substituting into R1:
$x - 3y/2 = 5/2 => x+3/2=5/2 => x=1$

How do you solve using gaussian elimination or gauss-jordan elimination, 2x - 3y = 52x−3y=52x - 3y = 5, 3x + 4y = -13x+4y=−13x + 4y = -1?