How do you solve the system #y - 2 z = - 6#, #- 4x + y + 4 z = 44#, #- 4 x + 2 z = 30#?

1 Answer
Dec 16, 2015

Answer:

#(x,y,z)=(-5,4,5)#

Explanation:

Given:
#{: ([1],color(white)("XXX"),,y,-2z," = ",-6), ([2],color(white)("XXX"),-4x,+y,+4z," = ",44), ([3],color(white)("XXX"),-4x,,+2z," = ",30) :}#

Subtract [3] from [2]
#{:([4],color(white)("XXX"),color(white)("XXX"),y,+2z," = ",14):}#

Subtract [1] from [4]
#{:([5],color(white)("XXX"),color(white)("XXX"),color(white)("XX"),+4z," = ",20):}#

Divide [5] by #4#
#{:([5],color(white)("XXX"),color(white)("XXX"),color(white)("XX"),z," = ",5):}#

Substitute #5# for #z# in [1]
#{:([6],color(white)("XXX"),color(white)("XXX"),y,-2(5)," = ",-6):}#

Add #10# to both sides of [6]
#{:([7],color(white)("XXX"),color(white)("XXX"),y,color(white)("XX")," = ",4):}#

Substitute #5# for #z# in [3]
#{:([8],color(white)("XXX"),-4x,color(white)("XX"),+2(5)," = ",30):}#

Simplify
#{:([9],color(white)("XXXXX"),x,color(white)("XX"),color(white)("XX")," = ",-5):}#