To solve the system of equations using the substitution method, we start with the given equations:
- \( y = 4x + 6 \)
- \( 3x + 2y = 12 \)
We will substitute \( y \) from the first equation into the second equation.
Substituting \( y \) into the second equation:
\[ 3x + 2(4x + 6) = 12 \]
Now, simplify the equation:
\[ 3x + 8x + 12 = 12 \]
Combine like terms:
\[ 11x + 12 = 12 \]
Subtract 12 from both sides:
\[ 11x = 0 \]
Now, solve for \( x \):
\[ x = 0 \]
Now that we have \( x \), we can find \( y \) by substituting \( x = 0 \) back into the first equation:
\[ y = 4(0) + 6 = 6 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (0, 6) \]
Therefore, the answer is:
(0, 6)
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