You have the system of linear equations:

1. $5x + y = 8$
2. $3x - 4y = 14$

We can solve this system using either substitution or elimination. I'll use substitution here.

Step 1: Solve for $y$ in the first equation.

From $5x + y = 8$, isolate $y$:

$y = 8 - 5x$

Step 2: Substitute $y = 8 - 5x$ into the second equation.

Now, substitute $y = 8 - 5x$ into the second equation $3x - 4y = 14$:

$3x - 4(8 - 5x) = 14$

Step 3: Simplify and solve for $x$.

Expand the equation:

$3x - 32 + 20x = 14$

Combine like terms:

$23x - 32 = 14$

Add 32 to both sides:

$23x = 46$

Now, solve for $x$:

$x = \frac{46}{23} = 2$

Step 4: Substitute $x = 2$ back into the first equation to solve for $y$.

Substitute $x = 2$ into $y = 8 - 5x$:

$y = 8 - 5(2) = 8 - 10 = -2$

Solution:

The solution to the system of equations is:

$x = 2, \quad y = -2$

Would you like a more detailed explanation or have any follow-up questions?

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Here are 5 related questions to expand on this:

1. How do you solve a system of linear equations using the elimination method?
2. What happens if there is no solution to a system of equations?
3. How do you solve a system of equations with three variables?
4. What is the graphical interpretation of the solution to a system of linear equations?
5. How can matrices be used to solve systems of equations?

Tip: When solving systems of equations, always check your solutions by substituting the values of $x$ and $y$ back into the original equations to verify the results.