# How do you solve the system of equations algebraically #3x-5y+z=9, x-3y-2z=-8, 5x-6y+3z=15#?

##### 1 Answer

Jul 8, 2017

#### Explanation:

#"using the process of elimination"#

#color(blue)" eliminating z"#

#3x-5y+z=9to(1)#

#x-3y-2z=-8to(2)#

#5x-6y+3z=15to(3)#

#(2)+2xx(1)larr" row operation"#

#7x-13y=10to(4)#

#(3)-3xx(1)larr" row operation"#

#-4x+9y=-12to(5)#

#color(blue)" eliminating x"#

#4xx(4)+7xx(5)larr" row operation"#

#11y=-44tocolor(red)(y=-4)#

#"substituting in " (4)#

#7x+52=10tocolor(red)(x=-6)#

#"substituting in " (1)#

#-18+20+z=9tocolor(red)(z=7)#

#color(blue)"As a check"" in " (2)#

#-6+12-14=-8rarr" True"#

#rArr(-6,-4,7)" is the solution"#