You can solve the system of equations using the method of elimination or substitution. Here, I'll use the elimination method.

The system of equations is:

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

Step 1: Add the two equations together

By adding the two equations, we eliminate $y$:

$(x + y) + (x - y) = 3 + 1$

This simplifies to:

$2x = 4$

Step 2: Solve for $x$

$x = \frac{4}{2} = 2$

Step 3: Substitute $x = 2$ into one of the original equations

Let's substitute $x = 2$ into the first equation:

$2 + y = 3$

Step 4: Solve for $y$

$y = 3 - 2 = 1$

Solution:

The solutions are: $x = 2, \quad y = 1$

Would you like further details or have any questions?

Here are five related questions for practice:

1. Solve the system: $x + 2y = 5$ and $x - 2y = 1$.
2. Find $x$ and $y$ for $x + y = 7$ and $x - y = 5$.
3. Use substitution to solve $3x + y = 9$ and $x - y = 2$.
4. Solve the system: $2x + 3y = 12$ and $4x - 3y = 6$.
5. Solve $x + y = 4$ and $2x - y = 3$.

Tip: When solving systems of equations, always check your solutions by substituting them back into the original equations.