To solve for the value of \( x \) using the equations provided, we can substitute one equation into the other.
We have:
- \( y = 2x + 1 \)
- \( x = 12 - 2y \)
First, let's express \( y \) in terms of \( x \) using the first equation. We have:
\[ y = 2x + 1 \]
Now we'll substitute \( y \) from the first equation into the second equation:
\[ x = 12 - 2(2x + 1) \]
Expanding this gives:
\[ x = 12 - 4x - 2 \]
Combining like terms:
\[ x + 4x = 12 - 2 \]
\[ 5x = 10 \]
Now, solving for \( x \):
\[ x = \frac{10}{5} = 2 \]
Now we can find \( y \) using the value of \( x \). Substitute \( x \) back into the first equation:
\[ y = 2(2) + 1 = 4 + 1 = 5 \]
So the values we found are:
- \( x = 2 \)
- \( y = 5 \)
Therefore, the final answers are:
- \( x = 2 \)
- \( y = 5 \)