Let's solve the system of linear equations:

1. $x + 4y = 6$
2. $x - y = 1$

Step 1: Solve one of the equations for one variable

From the second equation, $x - y = 1$, solve for $x$: $x = y + 1$

Step 2: Substitute into the first equation

Now, substitute $x = y + 1$ into the first equation $x + 4y = 6$: $(y + 1) + 4y = 6$ Simplify the equation: $y + 1 + 4y = 6$ $5y + 1 = 6$ $5y = 5$ $y = 1$

Step 3: Solve for $x$

Now substitute $y = 1$ back into the equation $x = y + 1$: $x = 1 + 1 = 2$

Final Solution:

$x = 2, \quad y = 1$

Would you like further details or have any questions?

Here are five related questions:

1. How do you graph this system of equations?
2. What is the significance of the solution in terms of the lines?
3. Can a system of linear equations have no solution or infinitely many solutions?
4. How do we solve larger systems of equations?
5. What happens if both equations are parallel?

Tip: Always check your solution by substituting the values back into the original equations.