How do you solve using gaussian elimination or gauss-jordan elimination, #3x - 10y = -25#, #4x + 40y = 20#?

1 Answer
Jul 7, 2017

Answer:

#color(brown)(((1,0,|,-5),(0,1,|,1)))color(blue)(=>((" "x=-5),(" "y=+1))#

Explanation:

Given:
#3x-10y=-25#
#4x+40y=20#

Using the requested method.

#[(color(white)(.)x," "y,|,color(white)(.)c color(white)(..))]#

#color(brown)(((3,-10,|,-25),(4,40,|,20)))#
#" "R_1xx4andR_2xx3#
#" "darr#

#color(brown)(((12,-40,|,-100),(12,120,|,60)))#
#" "R_2 - R_1#
#" "darr#

#color(brown)(((12,-40,|,-100),(0,160,|,160)))#
#" "R_2 -:160#
#" "darr#

#color(brown)(((12,-40,|,-100),(0,1,|,1)))color(blue)( =>y=1)#
#" "R_1 -:12#
#" "darr#

#color(brown)(((1,-10/3,|,-25/3),(0,1,|,1)))#
#" "R_1 +10/3R_2 #
#" "darr#

#color(brown)(((1,0,|,-5),(0,1,|,1)))color(blue)(=>x=-5)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check:
#3x-10y" "->" "3(-5)-10(1)" "->" "-15-10=-25#

Required solution is -25 so the values are correct