Solve each system by elimination and substitution. Give your final answer as a ordered triple?

Question

X - 2y + 3z = 10

2 x - 3y + 8z = 23

-x +3y - 2z = -9

Answer 1

first we can leave alone x in 1th ecuation so we have
x=10+2y-3z
then replace this in ecuation 2 and ecn 3... so we have
2(10+2y-3z)-3y+8z=23
20+4y-6z-3y+8z=23
y+2z=3...(*)...

-(10+2y-3z)+3y-2z=-9
-10-2y+3z+3y-2z=-9
y+z=1...(**)

so we can use this two ecuations we have now and solve
ecn (*) minos ecuation (**) so we have:
z=2 ... <---- first result
now we repace this in one in (*) or (**) whatever
y+2(2)=3
y+4=3
y=3-4
y=-1 ... <--------second result
Now we can replace z=2 and y=-1 in one of 1, 2 or 3 ecuation
X - 2(-1) + 3(2) = 10
X+2+6=10
X+8=10
X=10-8
X=2...<---- 3rd result
so the answer is X=2, y=-1 and z=2

Answer 2

Add equations 2 and 3:-
x + 6z = 14

3x - 6y + 9z = 30
-4x + 6y - 16z = - 46-----ADD
- x - 7z = - 16

x + 6z = 14
- x - 7z = - 16-----ADD

- z = - 2
z = 2

x + 6z = 14
x = 2

- 2 + 3y - 4 = - 9
3y = - 3
y = - 1

x = 2, y = - 1, z = 2

Answer 3

(2,-1,2)