To solve the system of equations for $x$ and $y$:

1. $x + y = 3$
2. $x - 3y = 11$

We can use the method of elimination to find the values of $x$ and $y$.

First, let's eliminate $y$ by subtracting the first equation from the second equation:

$(x - 3y) - (x + y) = 11 - 3$

This simplifies to:

$x - 3y - x - y = 11 - 3$ $-4y = 8$

Solving for $y$:

$y = \frac{8}{-4}$ $y = -2$

Now that we have the value of $y$, we can substitute it back into the first equation to find $x$:

$x + y = 3$ $x - 2 = 3$ $x = 3 + 2$ $x = 5$

So, the value of $x$ is $5$.

Would you like more details or have any questions?

Here are 8 relative questions to expand your understanding:

1. How do you solve a system of equations using the substitution method?
2. What is the graphical interpretation of solving a system of linear equations?
3. How do you determine if a system of equations has no solution or infinitely many solutions?
4. Can you solve the system using the matrix method (Gaussian elimination)?
5. What are the applications of solving systems of linear equations in real life?
6. How do you solve a system of nonlinear equations?
7. What is the determinant of a matrix, and how is it used in solving systems of equations?
8. How does the consistency of a system of equations relate to its solutions?

Tip: When solving systems of equations, always double-check your solution by substituting the values back into the original equations to ensure they satisfy both equations.