How do you solve using gaussian elimination or gauss-jordan elimination, $2 x + 3 y = - 2$ $2x + 3y = -2$ , $- 6 x + y = - 14$ $-6x + y = -14$ ?

Question

1899 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-11T14:42:21

$color(brown)(((1,0,|,+2),(0,1,|,-2)))$

$x=2 and y=-2$

Using the form:

$(x,y,|,"answer")$

$color(brown)(((2,3,|,-2),(-6,+1,|,-14)))$
$" "(-3)xxRow_1$
$" "darr$

$color(brown)(((-6,-9,|,+6),(-6,+1,|,-14)))$
$" "Row_1-Row_2$
$" "darr$

$color(brown)(((0,-10,|,+20),(-6,+1,|,-14)))$
$" "Row_1-:(-10)$
$" "darr$

$color(brown)(((0,+1,|,-2),(-6,+1,|,-14)))$
$" "Row_2-Row_1$
$" "darr$

$color(brown)(((0,+1,|,-2),(-6,0,|,-12)))$
$" "Row_2-:(-6)$
$" "darr$

$color(brown)(((0,+1,|,-2),(+1,0,|,+2)))$

Write in row echelon form

$color(brown)(((1,0,|,+2),(0,1,|,-2)))$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check that $x=2 and y=-2$

$2x+3y=-2" "->" "LHS->2(2)+3(-2)=4-6=-2$

$-6x+y=-14" "->" "LHS->-6(2)+(-2)=-14$

How do you solve using gaussian elimination or gauss-jordan elimination, 2x + 3y = -22x+3y=−22x + 3y = -2, -6x + y = -14−6x+y=−14-6x + y = -14?