How do you solve -3x-y=0, y-4z=15, x-2y+z=-10?

1 Answer
Jan 1, 2017

x=-1"; "y=3"; "z=-3

Explanation:

((x,y,z,|,-),(-3,-1,0,|,0),(0,1,-4,|,15),(1,-2,1,|,-10))
color(brown)(" "R_3+2R_2)
color(brown)(" "darr)

((-3,-1,0,|,0),(0,1,-4,|,15),(1,0,-7,|,+20))
color(brown)(" "R_1+3R_3)
color(brown)(" "darr)

((0,-1,-21,|,60),(0,1,-4,|,15),(1,0,-7,|,+20))
color(brown)(" "R_1+R_2)
color(brown)(" "darr)

((0,0,-25,|,75),(0,1,-4,|,15),(1,0,-7,|,+20))
color(brown)(" "R_1-:(-25))
color(brown)(" "darr)

((0,0,1,|,-3),(0,1,-4,|,15),(1,0,-7,|,+20))
color(brown)(" "R_2+4R_1
color(brown)(" "darr)

((0,0,1,|,-3),(0,1,0,|,3),(1,0,-7,|,+20))
color(brown)(" "R_3+7R_1
color(brown)(" "darr)

((0,0,1,|,-3),(0,1,0,|,3),(1,0,0,|,-1))
color(brown)(" "R_3+7R_1

x=-1"; "y=3"; "z=-3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("check")

-3x-y=0" " ->" " -3(-1)-3= 0 " "color(red)(larr"True")

y-4z=15" " ->" "3-4(-3)=15" "color(red)(larr"True")

x-2y+z=-10" "->""-1-2(3)-3= -10" "color(red)(larr"True")