Sure, let's solve the system of equations using the substitution method.
Given:
1. \( y = x - 6 \)
2. \( 3x + 2y = 8 \)
First, substitute \( y \) from the first equation into the second equation:
\[ 3x + 2(x - 6) = 8 \]
Now, simplify and solve for \( x \):
\[ 3x + 2x - 12 = 8 \]
\[ 5x - 12 = 8 \]
\[ 5x = 20 \]
\[ x = 4 \]
Now that we have \( x \), substitute it back into the first equation to find \( y \):
\[ y = x - 6 \]
\[ y = 4 - 6 \]
\[ y = -2 \]
So, the solution to the system of equations is \( x = 4 \) and \( y = -2 \).
