Let's solve the simultaneous equations provided:

1. $3y - x = 8$
2. $5y - 2x = 6$

We can solve these equations using substitution or elimination. I’ll use substitution for this case.

Step 1: Solve one equation for $x$

From the first equation, solve for $x$: $x = 3y - 8$

Step 2: Substitute into the second equation

Now substitute $x = 3y - 8$ into the second equation $5y - 2x = 6$: $5y - 2(3y - 8) = 6$ Simplify the equation: $5y - 6y + 16 = 6$ $-y + 16 = 6$ $-y = 6 - 16$ $-y = -10$ $y = 10$

Step 3: Substitute $y = 10$ into the first equation

Now, substitute $y = 10$ into the equation $x = 3y - 8$: $x = 3(10) - 8$ $x = 30 - 8$ $x = 22$

Final Answer:

The solution to the system of equations is: $x = 22, \quad y = 10$

Would you like a detailed explanation of any step, or have further questions?

Here are some additional related questions:

1. What are the steps to solve a system of linear equations using the elimination method?
2. How can you check the solution to a system of equations?
3. How do you solve a system of three linear equations with three variables?
4. What is the graphical interpretation of solving simultaneous linear equations?
5. How do you solve non-linear simultaneous equations?

Tip: Always double-check your substituted values to make sure the solution satisfies both original equations.