Answer:
x=5,y=2,z=-1
Step-by-step explanation:
x+y+z=6 ........1
2x-y+3z=5 ..........2
3x+2z=13 ⇒3x=13+2z ⇒ x=(13-2z)/3
substitute for x in equation 1 and 2
13-2z/3+y+z=6 ⇒13/3 -2z/3+y+z=6 ⇒z/3+y=6-13/3
z/3+y=5/3 first equation
2(13-2z)/3-y+3z=5
26/3-4z/3-y+3z=5⇒5z/3-y=5-26/3⇒
5z/3-y=-11/3 second equation
z/3+y=5/3 first equation
eliminate y
5z/3-y+z/3+y=-11/3+5/3
6z/3=-6/3
z=-1
x=(13-2z)/3 ( find x, bu substitute z=-1)
x=(13+2)/3
x=15/3 ⇒ x=5
x+y+z=6
5+y-1=6
y=6+1-5
y=2
