We are given the system of simultaneous equations:

1. $y = 4x + 3$
2. $6x + y = 8$

To solve this, we can substitute the expression for $y$ from the first equation into the second equation.

Step 1: Substitution

Substitute $y = 4x + 3$ into $6x + y = 8$:

$6x + (4x + 3) = 8$

Step 2: Simplify the equation

Combine like terms:

$6x + 4x + 3 = 8$

$10x + 3 = 8$

Step 3: Solve for $x$

Subtract 3 from both sides:

$10x = 5$

Now divide both sides by 10:

$x = \frac{5}{10} = 0.5$

Step 4: Solve for $y$

Now that we know $x = 0.5$, substitute this value into the first equation to find $y$:

$y = 4(0.5) + 3$

$y = 2 + 3 = 5$

Solution:

The solution to the system of equations is:

$x = 0.5, \quad y = 5$

Let me know if you'd like any further details or clarification.

Here are 5 related questions you might consider:

1. How can you verify the solution of a system of equations?
2. What are some methods to solve simultaneous equations besides substitution?
3. How would this problem change if the second equation were $6x + 2y = 8$?
4. What is the geometric interpretation of solving simultaneous linear equations?
5. Can simultaneous equations have more than one solution?

Tip: Always substitute your solution back into both original equations to verify its correctness.