Solve the following system of equations #[((1) " ", (2x + y + 3z = 12)),((2) " ",(4y – z = -7)),((3) " ",(5x + 8z = 34))]#?

1 Answer
Oct 22, 2016

Answer:

#x=2#
#y=-1#
#z=3#

Explanation:

#color(lightgreen)(( 1 )# #color(lightgreen)rarr# #2x+y+3z=12#
#color(lightblue)(( 2)# #color(lightblue)rarr# #4y-z=-7#
#color(pink)(( 3)# #color(pink)rarr# #5x+8z=34#

Using #color(lightblue)((2)#:
#color(orange)((4)# #color(orange)rarr# #z=4y+7#

Substituting the value of #z# in #color(pink)((3)#:
#5x+8(4y+7)=34#

#5x+32y+56=34#

#color(blue)((5)# #color(blue)rarr# #5x+32y=-22#

Substituting value of #z# in #color(lightgreen)((1)#:
#2x+y+3(4y+7)=12#

#2x+y+12y+21=12#

#color(purple)((6)# #color(purple)rarr# #2x+13y=-9#

Solving #color(blue)((5)# & #color(purple)((6)# simultaneously:
#5x+32y=-22#
#2x+13y=-9#

Multiply #color(purple)((6)# by #-2.5#:
#cancel(5x)+32y=-22#
#cancel(-5x)-32.5y=+22.5#

#-0.5y=0.5#

#color(red)(y=-1)#

Substituting value of #color(red)y# in #color(purple)((6)#:
#2x+13(-1)=-9#

#2x-13=-9#

#2x=4#

#color(red)(x=2)#

Substituting value of #color(red)y# in #color(orange)((4)#:
#z=4(-1)+7#

#z=-4+7#

#color(red)(z=3)#