x=8
y=-2
Z=3
Explanation
Step 1
Let
[tex]\begin{gathered} x+y+z=9\text{ Equation (1)} \\ x-z=5\text{ Equation(2)} \\ x+y=6\text{ Equation(3)} \end{gathered}[/tex]Step 2
isolate x from equation (1) , (2) and (3)
[tex]\begin{gathered} x+y+z=9 \\ x=9-y-z\text{ Equation (4)} \end{gathered}[/tex][tex]\begin{gathered} x-z=5 \\ x=5+z\text{ equation (5)} \\ \\ x+y=6 \\ x=6-y\text{ equation(6)} \\ \end{gathered}[/tex]Step 3
combining equation (4) and (5)
[tex]\begin{gathered} 9-y-z=5+z \\ 9-y-2z=5 \\ -y-2z=5-9 \\ -y-2z=-4\text{ Equation(7)} \end{gathered}[/tex]Step 4
[tex]\begin{gathered} x=x \\ \text{equation (5) = equation (6)} \\ 5+z=6-y\text{ equation (8)} \end{gathered}[/tex]Step 5
using equation(7) and (8) find y and z
[tex]\begin{gathered} -y-2z=-4\text{ (7)} \\ 5+z=6-y(8) \\ \text{isolate y from equation (7)} \\ -y=-4+2z \\ y=4-2z \\ \text{replace in equation (8)} \\ 5+z=6-4+2z \\ 5+z=2+2z \\ z-2z=2-5 \\ -z=-3 \\ z=3 \end{gathered}[/tex]replace the value of z= 3 in equation (7) to find y
[tex]\begin{gathered} -y-2z=-4 \\ -y-2\cdot3=-4 \\ -y-6=-4 \\ -6+4=y \\ y=-2 \end{gathered}[/tex]finally, replace the value of y in equation (3) to find x
[tex]\begin{gathered} x+y=6 \\ x-2=6 \\ x=6+2 \\ x=8 \end{gathered}[/tex]I hope this helps you