To solve the system of equations:
- \( x + 2y = 14 \) (Equation 1)
- \( y = 3x - 14 \) (Equation 2)
We can substitute Equation 2 into Equation 1.
Substituting \( y \) in Equation 1:
\[ x + 2(3x - 14) = 14 \]
Now distribute the 2:
\[ x + 6x - 28 = 14 \]
Combine like terms:
\[ 7x - 28 = 14 \]
Add 28 to both sides:
\[ 7x = 42 \]
Now divide by 7:
\[ x = 6 \]
Now that we have \( x \), we can substitute it back into Equation 2 to find \( y \):
\[ y = 3(6) - 14 \]
\[ y = 18 - 14 \]
\[ y = 4 \]
The solution to the system of equations is:
\[ (x, y) = (6, 4) \]