We are solving the system of simultaneous equations given in the image:

1. $y = 3x$
2. $5x - y = 6$

Step 1: Substitute $y = 3x$ into $5x - y = 6$

Replace $y$ in the second equation with $3x$: $5x - (3x) = 6$

Simplify: $5x - 3x = 6$ $2x = 6$

Step 2: Solve for $x$

$x = \frac{6}{2} = 3$

Step 3: Find $y$ using $y = 3x$

Substitute $x = 3$ into $y = 3x$: $y = 3(3) = 9$

Final Solution:

$x = 3, \, y = 9$

Let me know if you'd like further explanations or have any questions! 😊

Follow-up Questions:

1. What are the methods for solving simultaneous equations apart from substitution?
2. Can this pair of equations be solved graphically?
3. How do you identify dependent or inconsistent systems of equations?
4. How would the solution change if $y = 3x$ were replaced by $y = 4x$?
5. What are the real-world applications of solving simultaneous equations?

Tip: Always double-check your substitution to ensure no mistakes when replacing variables.