To solve the system of equations given by:
- \( y = 2x + 1 \)
- \( x = 12 - 2y \)
we can substitute the expression for \( y \) from the first equation into the second equation.
Starting with the second equation, substitute \( y \):
\[ x = 12 - 2(2x + 1) \]
Distributing the -2 gives:
\[ x = 12 - 4x - 2 \]
Combining like terms:
\[ x + 4x = 12 - 2 \] \[ 5x = 10 \]
Now, solve for \( x \):
\[ x = \frac{10}{5} = 2 \]
Now that we have \( x \), we can find \( y \) by substituting \( x = 2 \) back into the first equation:
\[ y = 2(2) + 1 = 4 + 1 = 5 \]
So the solution is:
\[ x = 2, \quad y = 5 \]