How do you solve this system of equations: #4x + 9y + 10z = - 138; 8x - 3y + 6z = - 94; 5x - 5y - 4z = 8#?

1 Answer
Nallasivam V
Feb 26, 2018

#x=-8#
#y=-4#
#z=-7#

Explanation:

Given -

#4x+9y+10z=-138# ----------------(1)
#8x-3y+6z=-94 # ----------------(2)
#5x-5y-4z=8 # ----------------(3)

Take equations (1) and (2)

#4x+9y+10z=-138 # ----------------(1) #xx 2#
#8x-3y+6z=-94# ----------------(2)

#8x+18y+20z=-276# ---------------(4)
#8x-3y+6z=-94# ----------------(2) ---- #(4)-(2)#
#21y+14z=-182# -------------------(5)

Take equations (1) and (3)

#4x+9y+10z=-138# ----------------(1) ------- #xx5#
#5x-5y-4z=8 # ----------------(3)----------#xx4#

#20x+45y+50z=-690 #----------------(6)
#20x-20y-16z=32# ---------------------(7)---#(6)-(7)#
#65y+66z=-722# -------------------(8)

Take equations #(5) and (8)#

#21y+14z=-182# -------------------(5) -----------#xx65#
#65y+66z=-722# -------------------(8) -------------#xx21#

#1365y+910z=-11830# -----------(9)
#1365y+1386z=-15162# ------------(10)----#(9)-(10)#
#-476z=3332#
#z=3332/(-476)=-7#
#z=-7#

Substitute #y=-7# in equation (5)

#21y+14(-7)=-182# -------------------(5)
#21y-98=-182#
#21y=-182+98=-84#
#y=(-84)/21=-4#
#y=-4#

Substitute #y=-4# and >#z=-7# in equation (3)

#5x-5(-4)-4(-7)=8 # ----------------(3)
#5x+20+28=8#
#5x+48=8#

#5x=8-48=(-40)/5=-8#
#x=-8#

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