To solve the system of equations given:
- \( y = x + 1 \) (Equation 1)
- \( 4x + y = 6 \) (Equation 2)
we can substitute Equation 1 into Equation 2.
Substituting \( y \) from Equation 1 into Equation 2:
\[ 4x + (x + 1) = 6 \]
Now simplify the equation:
\[ 4x + x + 1 = 6 \] \[ 5x + 1 = 6 \]
Next, subtract 1 from both sides:
\[ 5x = 5 \]
Now, divide by 5:
\[ x = 1 \]
Now that we have the value of \( x \), we can find \( y \) using Equation 1:
\[ y = x + 1 \] \[ y = 1 + 1 = 2 \]
Thus, the solution to the system of equations is:
\[ \boxed{(1, 2)} \]