Let's solve the system of equations:

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

Step 1: Add the two equations to eliminate $y$

We can add the two equations directly because the terms involving $y$ will cancel out:

$(x + y) + (3x - y) = 1 + (-5)$

Simplifying both sides:

$x + 3x + y - y = 1 - 5$

$4x = -4$

Step 2: Solve for $x$

Now, divide both sides by 4:

$x = \frac{-4}{4} = -1$

Step 3: Substitute $x = -1$ into the first equation

Substitute $x = -1$ into the equation $x + y = 1$:

$-1 + y = 1$

Solving for $y$:

$y = 1 + 1 = 2$

Final Solution:

The solution to the system of equations is: $x = -1, \quad y = 2$

Would you like a more detailed explanation or further questions on this topic?

Here are some related questions:

1. How can we check the solution to a system of equations?
2. What would happen if we had an additional equation?
3. How can this system of equations be solved using substitution?
4. How do we solve a system of equations when there are more than two variables?
5. What are some applications of solving systems of equations?

Tip: To solve systems of equations, it's often useful to eliminate variables by adding or subtracting the equations, making the solution process quicker!