The question appears to ask for the values of $x, y,$ and $z$ based on a set of linear equations. Let me extract the details from the image to analyze and solve the equations.

Here are the equations extracted:

1. $2x + y + 3z = 3$
2. $x + 5z = -2$
3. $z = -1$

Now, let's solve for $x, y,$ and $z$:

Step 1: Substitute $z = -1$ into the other equations

From Equation (3), $z = -1$.

Substitute $z = -1$ into Equation (2):

$x + 5(-1) = -2$ $x - 5 = -2 \quad \Rightarrow \quad x = 3$

Substitute $z = -1$ and $x = 3$ into Equation (1):

$2(3) + y + 3(-1) = 3$ $6 + y - 3 = 3 \quad \Rightarrow \quad y = 0$

Final Solution:

$x = 3, \; y = 0, \; z = -1$

Would you like me to verify these values or explain the steps in more detail?

Here are 5 related questions for further practice:

1. What is the determinant of the coefficient matrix of these equations?
2. How would the solution change if $z \neq -1$?
3. Can you graphically interpret the solution of these linear equations?
4. How would you use matrix methods to solve these equations?
5. What if one equation is removed—how would you find the solutions in terms of parameters?

Tip: Always substitute back the variables to verify your solution in all equations.