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

##### 1 Answer

Sep 27, 2016

#### Explanation:

Given:

#x+y+z = 105#

#10y-z = 11#

#2x-3y = 7#

Add the first two equations together to eliminate

#x+11y = 116#

Multiply this equation by

#2x+22y = 232#

Subtract the original third equation to eliminate

#25y = 225#

Divide both sides by

#color(blue)(y = 9)#

Substitute this value of

#2x-27 = 7#

Add

#2x = 34#

Divide both sides by

#color(blue)(x = 17)#

Substitute the values for

#17+9+z = 105#

Subtract

#color(blue)(z = 79)#