We are solving the system of equations:

1. $x + y = 14$
2. $y = 6x$

Step 1: Substitute $y = 6x$ into $x + y = 14$

Substituting $y = 6x$ into the first equation:

$x + 6x = 14$

Step 2: Simplify and solve for $x$

$7x = 14$ $x = 2$

Step 3: Solve for $y$

Using $y = 6x$ and substituting $x = 2$: $y = 6(2) = 12$

Final Solution:

$x = 2, \, y = 12$

Would you like more details or have any questions?

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Here are 5 related questions for practice:

1. Solve the system of equations $2x + y = 10$ and $y = 3x$.
2. If $x + y = 20$ and $y = 4x$, what are the values of $x$ and $y$?
3. Solve for $x$ and $y$ if $3x + 2y = 18$ and $y = 5x$.
4. What is the solution to $x - y = 5$ and $y = -2x$?
5. Solve the system $x + y = 0$ and $y = -3x$.

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Tip: When solving systems of equations, substitution is helpful if one variable is already isolated in terms of the other.