How do you solve this system of equations: #3x - 3y + 5z = 13 , 3x + y - 3z = - 5 and 19x - y - 5z = 0#?

1 Answer
Tamir E.
Dec 26, 2017

#x=1/2#
#y=-1/2#
#z=2#

Explanation:

#3x-3y+5z=13#
#3x+y-3z=-5 iff y=-3x+3z-5#
#19x-y-5z=0 iff y=19x-5z#
#=>#
#3x-3(-3x+3z-5)+5z=13#
#3x-3(19x-5z)+5z=13#
#=>#
#3x+9x-9z+15+5z=13#
#3x-57x+15z+5z=13#
#=>#
#12x-4z=-2 iff z=3x+1/2#
#-54x+20z=13#
#=>#
#-54x+20(3x+1/2)=13#
#=>#
#-54x+60x+10=13#
#=>#
#6x=3#
#=>#
#x=1/2#
#=>#
#z=3(1/2)+1/2=2#
#=>#
#y=-3(1/2)+3(2)-5#
#=>#
#y=-1/2#

Check (with a calculator):
#3(1/2)-3(-1/2)+5(2)=13#
#3(1/2)+(-1/2)-3(2)=-5#
#19(1/2)-(-1/2)-5(2)=0#
Worked! :)

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