Question 1028392
x = 2 is correct.
Using the first two equations 4x+5y+z=23, 2x-5y-z=-11
If we add the two equations we get
6x = 12
so x =2
We now need two equations to solve for the other two variables.
Let's use 4x+5y+z=23 and 3x+y+3z=-5
If we substitute 2 for x in each, we have
4(2)+5y+z=23 and 3(2)+y+3z=-5
8 + 5y + z = 23  and  6 + y + 3z = -5
Add -8 to each side of the first equation and -6 to each side of the other.
5y + z = 15 and y + 3z = -11
Rewriting
5y + z = 15
y + 3z = -11
Multiply the top equation by -3
-15y - 3z = -45
y + 3z = -11
Adding the two equations we get
-14y = -56
y = 56/14
y = 4
To find z, substitute 4 for y in y + 3z = -11
4 + 3z = -11
add -4 to each side
3z = -15
divide each side by 3
z = -5
We have x = 2 , y = 4 , z = -5
Notice that with the following input to www.wolframalpha.com
4x+5y+z=23; 2x-5y-z=-11; 3x+y+3z=-5 ,
you can obtain the solution.