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

1 Answer
Jun 11, 2017

Answer:

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

#x=2 and y=-2#

Explanation:

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#