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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.

Solve the following simultaneous equations: y = 4x + 3 and 6x + y = 8

Learn how to solve the system of simultaneous equations y = 4x + 3 and 6x + y = 8 using the substitution method. This problem explores key algebraic concepts and is suitable for students in Grades 8-10.

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