How do you solve the system of equations: #x+y+z = 105#, #10y-z = 11#, #2x-3y = 7# ?

1 Answer
Sep 27, 2016

Answer:

#x=17#, #y=9# and #z=79#

Explanation:

Given:

#x+y+z = 105#

#10y-z = 11#

#2x-3y = 7#

Add the first two equations together to eliminate #z# and get:

#x+11y = 116#

Multiply this equation by #2# to get:

#2x+22y = 232#

Subtract the original third equation to eliminate #x# and get:

#25y = 225#

Divide both sides by #25# to get:

#color(blue)(y = 9)#

Substitute this value of #y# into the third equation to get:

#2x-27 = 7#

Add #27# to both sides to get:

#2x = 34#

Divide both sides by #2# to get:

#color(blue)(x = 17)#

Substitute the values for #x# and #y# into the first equation to get:

#17+9+z = 105#

Subtract #26# from both sides to get:

#color(blue)(z = 79)#