How do you solve these system of equations: #x+ y + 3z = 7;x - y + z = - 5;x + 2y - 2z = 37#?

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Answer 1 · 2017-07-05T10:35:21

Solution: #x=9 , y = 10 ,z=-4#

#x+y+3z=7 ; (1) , x-y+z= -5 (2) ; x +2y-2z = 37 (3)#

#x= 7-y-3z# . putting #x= 7-y-3z# in equation (2) we get,

# 7-y-3z -y +z = -5 or 2y +2z =12 or y+z =6 (4) #

putting #x= 7-y-3z# in equation (3) we get,

# 7-y-3z +2y -2z =37 or y-5z =30 (5)# .

Subtracting equation #(5) #from # (4)# we get

# 6z= -24 or **z = -4** :. y =6 -(-4) or **y=10** :. x = 7 -10 -3*(-4) = 7 -10+12 or **x=9** #

Solution: #x=9 , y = 10 ,z=-4# [Ans]